How was it concluded that Jupiter and Saturn are gaseous planets without a solid surface (if we are not yet able to interact with their atmospheres)?

“(if we haven’t been able to interact with its atmosphere yet)?”

You are making the Galileo Probe cry, which entered Jupiter’s atmosphere. The Galileo Probe was able to send back data on Jupiter’s atmosphere for 70 minutes and then overheated, gave in to pressure and burned up.

How was it concluded that Jupiter and Saturn are gaseous planets without a solid surface?

There are many clues that allow us to ignore that these two planets lack a solid surface and there are other clues that are a little more difficult to interpret.

First, we know what the density of Jupiter and Saturn is. We know their diameters. And thanks to the orbital periods of their moons (which depend on the mass of the planet), we can estimate the masses of the planets. If we know the diameter (which allows us to know the volume) and the mass, we can calculate the density, in fact:

• Jupiter’s density is slightly higher than that of water: 1.33 g/cm^3.
• Saturn’s density is less than that of water: 0.687 g/cm^3.

The only thing that could explain these densities is that they are composed of gas, which is usually in the form of compressed fluids (hydrogen superfluid) or low-density solids (metallic hydrogen).

Second, thanks to spectroscopic studies of the composition of the planets, we know the composition of the atmosphere of Jupiter and Saturn. A telescope, equipped with a spectrometer, can determine that they are composed almost exclusively of hydrogen and helium. 

As additional data, the Galileo Probe measured the composition of Jupiter’s atmosphere directly.

Third, thanks to the gravitational studies of the Juno and Cassini probes, we have been able to measure the mass distribution of both planets. (Because the planets have an uneven distribution of their mass – since it concentrates as we get closer to their core – a space probe will experience a variable acceleration due to its force of gravity.) For example, precision instruments of the Juno probe allowed us to know more about the diffuse nucleus of Jupiter.

In summary, Saturn and Jupiter are composed mostly of hydrogen (according to spectroscopic studies) and these substances become liquid and solid at high pressures, this contributes to these planets having a low density. And it leads us to build diagrams like the one shown below: