Some of it already has.
The Cell Phone is reality TODAY, because the President of Motorola wanted to have a "communicator" like Cpt. James Kirk's from the original series. I STILL have a good old reliable Flip-Fone.
The medical beds from the original Star Trek are ALMOST a reality in today's modern hospitals. Although the patient is still hooked up using wires and sensors, the electronic signals are displayed on computer screens beside the bed, and the data can be transmitted to computers in the Nurses Station dozens of feet away.
Phasers are not in existence, but burning and cutting lasers are -- but not as weapons. The laser weapons platform is still non-existent, but you may expect to see them in the next 50 years.
You can get an almost-pretty-good Universal Translator as an "add in" to your Web Browser or Microsoft Word. Being able to TALK to a computer has been a reality for a long time, but getting it to understand you AND respond in an innocuous female voice is as close as your Smart-phone and Siri.
We still can't have Scotty "beam us up". That is a VERY difficult task. But research shows that it may be possible using inanimate, non-living objects in the next 300-500 years.
Warp Drive is still missing two of its key components -- the Graviton (the particle by which gravity energy is transferred), and a power source powerful enough to produce them. Dilithium is, of course, a myth, but that's OK -- dilithium FOCUSES the energy, but it does not PRODUCE the energy.
[There is simply NO anti-matter in existence. It can be made only ONE atom at a time using a Super-collider. But when ONE atom is made, it almost immediately collides with an atom of matter, and annihilates itself before it can be "captured" and stored. While Einstein's Equation has been proven true, only two atoms is still a VERY tiny amount of energy.]
Anti-gravs, force fields, cloaking devices, and things like that have already proven themselves to be MUCH harder to make than to dream about. But these devices are much more likely to come true before the fabled Warp Drive can be brought into existence.
CAN Star Trek become a reality? Maybe. WILL it become a reality? Probably not, at least not until well after the 24th Century (about 300 years from now) time frame when Star Trek takes place.