If the aliens are a few years ahead of us and use the same basic principles that we do, you'll be fine. Except we already know that they have at least some tech that we don't have, and clearly they have some branches of science that we know nothing about or they wouldn't be flying spaceships around the galaxy.
Worse, we don't have access to their knowledge about things like materials science, manufacturing processes, etc. All we have is some of the products of their technology to examine. Sure, we can put bits in a spectrograph and figure out what it's made of, but that doesn't tell us how it's made. We have plenty of examples in our own history of things made with lost techniques, like the very best Samurai blades from ancient Japan. After many decades of study and attempts to replicate them, we still can't reproduce the work of the master swordsmiths like Motoshighe, Tadayoshi and Masamune. We can know everything about the composition of the materials, but the production methods - in an age where hitting metal with other chunks of metal was the height of technology - are unknown to us.
For a more recent example, there are plenty of companies that use proprietary techniques to make their products. A lot of the time they won't even patent their processes, preferring to gamble on the chance that nobody will be able to figure out the process independently. Some tiny trick that their researchers found that enables them to produce something new, or even produce something old in a new way, and they know that only the same lucky break by a talented researcher is going to figure it out. And these people all share the same basic science and technology.
Now let's look at your alien ship. Start with something simple: the hull plates. Lightweight, extremely high tensile strength, good thermal conductivity and so on. We can run a piece through a spectrograph, do some crystallography, maybe a few other things to figure out what it's made from. But we can never figure out that the reason it's so strong is that the alien shipyard casts the alloy and uses some weirdly distorted electromagnetic fields to encourage the growth of cross-aligned crystalloid filaments in the metal during a quenching phase. We can make the alloy by the ton but it's no more useful for armor than plain aluminium sheet.
Things get worse from there. The power distribution systems on the ship use an insulator that we can't even figure out the basis for, other than that it appears to be a long-chain polymer of some sort. It's produced by a gene-tailored creature similar to a silk worm, then treated by an enzyme produced by synthetic bacteria in... and so on. Each step of the process to create the insulator requires technologies we don't have access to, and even if we did we still don't know the process.
The FTL drive? Not only does it work on principles of physics we never even heard of, is made from materials we can't even examine, but there's some weird spatial distortion thing going on that we can't quite explain. All we know is that every time we bring a screwdriver near the damned thing it turns into a pretzel before disintegrating.
Under those conditions? Sorry, we're looking at a couple of centuries of work and some very, very good bits of luck on the way.
Your only real option to get it done quick is if the renegade aliens have enough knowledge and are willing to teach it to you. Better make nice with them pretty quick.
Sorry, this isn't an HFY-friendly answer, and it kind of spits in the face of shows like Stargate, but humans just aren't going to suddenly make some sort of leap just because they have some busted up spaceships to work with. I mean, like, we've had those alien ships at Area 51 for, what, half a century? Where's my hoverboard???