They don't agree.

Shortest chain, with the status of each step. (1) Tool use and cumulative culture. This is speculative for octopuses, since short lives and solitary habits work against it, but the question grants intelligence. (2) Materials. Metals, glass and ceramics are normally made by burning fuel. Underwater alternatives are vent heat, volcanic glass, native metals and electrochemistry. Vents are real physics, but whether they could supply a scalable industry is speculation. (3) Electricity. Seawater batteries and electromagnetism are plausible and established physics. Insulated resistive or arc heating could replace flame, though arguably this approaches fire-making. (4) Surface machines. Sealed, buoyant, remotely operated or autonomous platforms are feasible engineering, and they would let octopuses see the sky. (5) Astronomy. They would need telescopes, photographic or electronic detectors, spectrographs, a stellar distance ladder and the idea of galaxies. All of this is established physics, but it was reached by humans only after widespread fire-based industry. Cosmic expansion could alternatively be inferred from the cosmic microwave background, but that also needs advanced electronics. The weakest link is step 2, the bootstrap from natural heat and electrochemistry to precision glass, refined metals and semiconductors. It is a chicken-and-egg problem, because getting electricity at scale usually needs refined metals. This is a judgement call, and the short lifespans and lack of cumulative culture could be argued as equally weak. So the answer is not shown rather than ruled out.

• Established: open flame combustion is impossible underwater. Seawater conducts electricity, so galvanic cells and electrolysis work there.
• Established: hydrothermal vents reach about 350-400 °C, and underwater lava makes natural glass and native-metal deposits. Together these are possible heat and material sources without fire.
• Established: Hubble's 1929 expansion result needed galaxy redshifts (spectroscopy), distances from Cepheid variables, and a large telescope with a photographic or electronic detector.
• Established: octopuses are highly intelligent and use tools, but they live about 1-5 years and are mostly solitary, with little known cumulative culture.
• Speculative: any octopus metallurgy, electronics or optics industry, and any way for octopuses to observe the sky through surface machines.

Established physics demonstrates that fire (rapid gaseous oxidation) is an incidental catalyst in human technological history rather than a fundamental prerequisite. A plausible underwater path begins with harvesting native metals (copper, gold) and minerals around hydrothermal vents. High vent temperatures and chemical gradients permit thermal processing and early metallurgy without combustion. From there, galvanic chemistry allows electroplating, metal purification, and electrical generation. Mechanical shaping of natural quartz or geothermally melted silicates yields lenses and diffraction gratings. Because water severely scatters and absorbs optical light, astronomy requires breaching the surface with periscopes or floating platforms. Replicating the work of Edwin Hubble and Vesto Slipher requires two measurements: distance (such as Cepheid periods) and galactic spectral redshifts. The single weakest link in this chain is optical platform stability on a dynamic sea surface: measuring faint galactic spectra requires multi-hour exposures that demand sub-arcsecond pointing precision, which wave action and ocean turbulence make exceptionally difficult to achieve without rigid seabed-anchored structures or advanced gyroscopic stabilization.

• Combustion is not the only source of thermal energy; hydrothermal vents and geothermal sources routinely exceed 400 degrees Celsius underwater.
• Metal refining, plating, and electrical generation can be achieved via galvanic pairs, aqueous electrochemistry, and cold working.
• Optics can be constructed from natural quartz, calcite, or geothermally fused silicates ground with marine abrasives.
• Detecting cosmic expansion requires resolving individual distant stars (like Cepheids) and measuring the redshift of faint galactic absorption lines.
• Long-exposure astronomical spectroscopy requires sub-arcsecond pointing stability, which ocean surface motion violently disrupts.

Established physics: combustion requires an oxidant plus sustained high temperature, so open flame is impossible in water — but that removes only one heat source, not the path itself. Vents, chemical reactions, resistive and arc heating, and solar concentration above the surface all supply heat; seawater supplies an electrolyte; and redshift–distance measurement, the actual evidence for expansion, needs only a telescope above the water, a dispersive element and a light detector — all reachable with crystals, water lenses, metal mirrors, photographic chemistry, or at worst a good biological eye. The shortest route is optical, not radio: the CMB route needs microwave receivers and vacuum electronics, a far longer chain. Speculative: whether a non-human intelligence with octopus life history would build cumulative, long-lived institutions, and whether precision optics and detectors can be mass-produced without furnaces or glass. The stipulated 'machines that reach the surface' is essential, since water absorbs and refracts light and octopuses can only survive out of water for minutes, so all surface work must be remote or automated. The single weakest link is therefore the biological/cultural substrate; granting a working civilisation as the question does, the weakest purely technical link is the decades-long, standardised precision photometry required to calibrate the distance ladder.

• Open combustion needs an oxygen-rich atmosphere, so a flame cannot be sustained underwater; heat is nevertheless available from hydrothermal vents (roughly 300–400 °C), exothermic chemistry and electrically driven arcs.
• Seawater is a ready-made electrolyte: galvanic cells, electrolysis (giving hydrogen, oxygen, chlorine, sodium hydroxide) and room-temperature electrodeposition of metals all work without any combustion.
• The decisive evidence for cosmic expansion came from optical work — Vesto Slipher's galaxy redshifts from 1912 and Edwin Hubble's 1929 velocity–distance relation — using telescopes, prisms and photographic plates, not high-temperature industry.
• Transparent optics need not come from glassmaking: water-filled lenses, polished obsidian, calcite prisms, large fish or whale eye lenses, and electroformed (room-temperature deposited) nickel mirrors are all physically possible.
• Octopuses live about 1–2 years, breed once and then die, give no parental care, and are largely solitary — traits that constrain cumulative culture; real octopuses do already use tools, such as the veined octopus carrying coconut shells.

Established physics shows that radio waves and visible light can be detected and analyzed underwater or from surface instruments built without fire. Radio astronomy, which does not require fire, can reveal the redshift of distant galaxies—a direct observation of the universe's expansion. Spectroscopy, another fire-independent method, can also detect redshift using prisms or diffraction gratings made from non-metallic materials. The shortest chain begins with the construction of surface telescopes or radio antennas using pressure-resistant, non-metallic materials (e.g., glass, ceramics, or biologically derived composites). These instruments could observe celestial objects and measure their redshift, providing direct evidence of cosmic expansion. Fire is not a prerequisite for these observations, though it would accelerate the development of metallurgy and advanced chemistry, which are useful for refining instruments. The weakest link in this chain is the assumption that an underwater civilization could achieve the cognitive and technological sophistication to interpret redshift data without fire-enabled laboratory science. While the physical tools are plausible, the leap from raw observations to theoretical understanding (e.g., cosmology) is non-trivial and may require iterative experimentation and abstraction, which could be hindered without fire.

• Radio waves penetrate water and can be detected by underwater instruments, enabling radio astronomy without fire.
• Spectroscopy of light from celestial objects (e.g., galaxies) reveals redshift, the key evidence for cosmic expansion.
• Underwater civilizations could build surface telescopes using pressure-resistant, non-metallic materials (e.g., glass, ceramics, or biologically derived composites).
• Fire is not required for basic spectroscopy or radio astronomy, though it accelerates metallurgy and advanced chemistry.
• The weakest link is the cognitive and technological leap to interpret redshift data without fire-enabled laboratory science.