Yes, but there's a few prerequisite technologies that we need to figure out before it will happen.

The key tech in my mind is:

• Fusion energy
• Near complete mastery of bioengineering
• Major space manufacturing

Need fusion energy for propulsion and powering the habitat.

Bioengineering is a catch all here for mastery of genetics and gene editing, artificial wombs, construction of artificial ecosystems, organism engineering, suspending animation, etc. We'll need to engineer ourselves and the things we wan't to eat to do well in low gravity and high radiation among other things. Extending lifespan into the 200+ year range and/or making suspending animation possible will help with motivating people to make the journey. Probably need artificial wombs as I can see pregnancy and birth on a spaceship being an issue.

Need to be able to build a big ship AND fix it along the way. If you're gonna have a self sustaining population of humans on this thing thats a huge ship with tons of redundancy needed for every system. You can't realistically build that by launching a bunch of little things into space on separate rockets, probably need asteroid mining and automated in-orbit construction around Earth or the moon. You also need to bring this capability with you if you want to do anything meaningful at your destination.

Basically once we're at a point where a lot of people already live in big o'neill cylinders around Earth some group of adventurous/crazy people will stick a few fusion rocket engines on one and head for the stars. It'll be good that they're already in a self-sustaining space habitat because the planet they go to is likely to suck, and they're gonna spend another 1000+ years in orbit seeing if von neumann probe-type robots and engineered microbes can get the planet somewhat livable.

Probably 100+ years before any human interstellar journey can even be considered.