Will humans ever come across Sentient Aliens?
No
Yes
Point for "yes": the universe is so big I think it's very unlikely that we're the only sapient species in it. Even if there was only one sapient species per galaxy there'd be billions of sapient species in the observable universe.
Point for "yes": the parts of the Drake Equation we have some information about seem to point toward life probably being common. The sun is a pretty common type of star. Planets seem to be pretty common. There's a planet around Proxima Centauri that gets about as much light as Earth and is about the same mass as Earth (it orbits a flare star, so it's probably not actually very friendly to life, but its cosmic proximity suggests planets like that are very common). If terrestrial planets are common, the basic recipe that produced life on Earth (liquid water + energy + complex chemistry) is probably very common in the universe, and it exists or existed on at least four worlds in our own solar system (Earth, Europa, Enceladus, and ancient Mars). Life seems to have got started on Earth pretty much as soon as Earth had conditions conducive to it, which suggests if you have conditions conducive to it for a billion years or so abiogenesis will probably happen.
Point for "no": the Fermi Paradox suggests a significant possibility that the nearest sapient aliens are so far away we'll never meet them or interstellar travel is so difficult it's basically completely impractical (either flat out impossible or the reward to effort ratio is so low even the most determined civilizations give up on it very quickly). Real science suggests interstellar travel is indeed formidably difficult, to the point that "we're living in a universe where interstellar travel on any significant scale is basically impossible" seems pretty plausible.
Point for "yes," kind of: even if physical interstellar travel is impossible, interstellar communication would be much easier. IIRC, we could talk to a technologically advanced civilization on a world orbiting a distant star with the technology and actually existing equipment we have now, if we knew where to point our radio telescopes and had the patience for a conversation in which receiving a reply would take years to millennia. So, even if we never physically meet sapient aliens, we may get to talk to them. Even a universe where physical interstellar travel is impossible may have a thriving galactic community of technologically advanced civilizations who communicate with each other by radio (if so, we're probably excluded from this network only because there hasn't yet been time for our nearest neighbors to receive our radio leakage and send a greeting and their first message to reach us; could happen any day now!). Also, even in a universe like that, with sufficiently advanced technology we might one day meet aliens in a way, by reconfiguring human intellects into a format that can be encoded into a radio transmission and sending them to the aliens, who could then run these posthuman minds on their own computers (and vice versa, some of the aliens could experience life on Earth this way). I think it's likely that we'll have the technology to do that within a few centuries, and it's likely that many of the alien civilizations, most of which would probably be much older than ours, would have the technology to do that.
Wait, you're asking about sentient aliens, not sapient aliens. So, like, would the Foundation and Dune sci fi settings, where we've never met sapient aliens but we have encountered lots of aliens analogous to nonhuman animals on Earth, count as universes where we met aliens for this question? I think meeting sentient but non-sapient aliens is more likely than meeting sapient aliens if interstellar travel is feasible (though if it's not getting to talk to sapient aliens is more likely; a radio transmitter with interstellar range is much easier to build than a starship, but having a conversation with someone in another solar system through radio transmissions requires people smart enough to build radio transmitters who know about radio at both ends). There's no Fermi Paradox for sentient but non-sapient aliens, and "sentient aliens are common but sapient aliens are rare" is, I think, one of the more plausible possible resolutions of it.
I rounded all this off to "Yes."












