Depends on what you mean IMO. You can’t accelerate to the speed of light, but current cosmology predicts “inflation” after the Big Bang that moved things apart faster than the speed of light by creating space between them. I think that is the most likely route we have some clue about today for getting around the speed of light limit. If we don’t nuke ourselves or suffer some other collapse of civilzation, they might crack this nut in a few more centuries or eons...
Not being Sheldon Cooper, I can't really keep up with the physics or math required to really understand this stuff, though I've always found it to be interesting. I've always suspected that inflation was hand waving by physicists to make up for the fact that they can't really explain what happened that soon after the big bang.