Proxima Centauri is 4.23 light years away (not 4.22 million ly away). At SOL, if you started today, you'd get there around 4 years and 84 days from now, which is December 6, 2023
Quarter that and it's still a fairly reasonable amount of time to travel, particularly if your crew can sleep through the trip. Then your arrival would be 16 years and 336 days from today, also known as right around August 15, 2036
The SOL in mph is 6.702 x 108 miles/hr. See: https://www.thoughtco.com/speed-of-light-in-miles-per-hour-609319
One-quarter of that is 167,550k mph by my math (if I'm wrong, please tell me).
The current fastest man-made object is the Parker Solar Plus. See: https://solarprobe.gsfc.nasa.gov/
It clocks in at a pretty impressive 450k mph.
So to get to 1/4 SOL, you'd need to multiply the Parker feat by a factor of 372.3. Again, if my math is wrong, please let me know.
So we can't do it yet
. But 1/4 SOL could happen, and I suspect it'll happen within a century. It's not zippy Star Trek speeds. But it still gets humans to another star system and back, with a fighting chance of there being plenty of people still around who were alive when the crew left.