A few hundred years?
In a few hundred years, we'll be lucky to be accomplishing what Arthur C Clarke suggested in 2001. We'll be lucky if we have a fully colonized lunar base with thousands of people and a reasonable support infrastructure. We'll be lucky if we have manned interplanetary spacecraft capable of generating gravity via centripetal force. We'll be lucky of those spacecraft have facilities for self sustainability in regards to food production and waste management. We'll be lucky if those spacecraft are capable of even 1% of c-travel (50k-mph is only about 14 miles per second, light speed is 186,000 miles per second... one percent would be 1860 miles per second... we need to be able to travel 132x faster than we can now to achieve 1% of light speed). We'll be lucky to have a deep space mining or factory industry.
The tech from the new V series is thousands of years advanced from us.
The tech from BSG is thousands of years advanced from us (FTL drive is essentially creating a wormhole).
Star Trek, ignoring the Warp Drive tech, is a good 500 years away.
The Fithp from Footfall were the least advanced alien species conqueror I think I've ever heard of in sci-fi.
Most of these are economic and political stagnation issues, not ones of actual knowledge or capability. At least in terms of interplanetary travel and bases within our Solar System. If the desire to do so existed, we'd be nicely comparable to a 2001 level of tech as depicted in the movie. (HAL excepted, OTOH, I bet the
hardware HAL runs on as imagined, in terms of pure flops per second, is inferior to the best systems of today...)
I also believe in accelerating technological progress. How the computer drives almost all our other advancements in biology, chemistry, materials science, astronomy, space flight etc. and the disciplines can reinforce one another.
If the ever increasing pace of change does not destroy a civilization, what you're thinking of as 500 or 1000 years of tech is quite possibly IMO, more like 50 to 100. I'm not sure humanity even will even experience a "Star Trek"-like phase.
The problem is not our tech, but the will to apply that tech to space exploration, exploitation, and colonization. If the economic and political will to do so does not exist, they won't happen.
OTOH, much like the spread of computer technology, perhaps as other technologies follow and flow down to the end-user, or business, we'll see an acceleration of the ability of those who want to go, to actually go.
I Had the K-T event not happened...it's likely small-to-medium dinosaurs would be the intelligent, dominant form of life here, but considering complex animals have only existed for less than 5-10% of our planet's life, and intelligence (pack hunters, etc) for less than a quarter of that, and cognitive intelligence for less than 1-2% of that, encountering something more advanced than primitive animals is a slim chance. On the other hand, humans have had fire and tools for about one-millionth of the planet's life, and complex tools for even less. Imagine how we would look to cavemen...encountering an alien population merely one-one millionth of it's planet's life further along is the difference between arrowheads and fire to mini guns, aircraft and lasers, or the difference between the latter and...what? Considering the singularity (in terms of computing, genetic engineering, nano tech, etc) is less than 100 years away...I say I hope we don't meet aliens HERE, because it would likely bode poorly for us.
That is a major hole in the Drake Equation. And one answer we'll never get from the likes of Mars or Europa (unless we find sentient fish under the ice or whatever..)
The late KT dinosaurs seemed to be trending towards agile bigger brained ostrich/emu like predators, but there's no real evidence that they'd ever develop into sentient/sapient tool users. Looking at the most successful phylum, the arthropods would argue against intelligence being some kind of "goal" or "end game" of evolution at all.
Unfortunately for us, right here, and right now, the only way to get these answers, and defend ourselves if need be is to "hang on" and grow as a species.
Although under this all, that's my main gut feeling as to why the Universe is so "quiet". Technological Singularities take every species off the table. Either through extinction when they're managed badly or not at all, or even when successful, off to other paradigms where exploration, colonization, much less conquest/war make no sense and are just irrelevant.
If you've seen that one episode of ST:TNG, my worry is that post-singularity life/intelligence is that it's like the visual analogy of the bored "Q" lounging about in a parlor. One reading a thick book titled "The Old", one reading a disappointingly thin, and rather vapid looking magazine titled "The New", and another playing billiards with balls that upon closer inspection are planets.