I think you meant to say intragalactic interstellar. But no, we will likely become interstellar when we are more mature.
Discussion
Yes, becoming intergalactic is impossible not just today, but also in the future. Milky way is roughly 100k light years in diameter, so light traveling at 186k miles per sec would still need 100k yrs to go from one side to the other. So yeah, we’re not leaving anytime soon 🤣