I've had (and still have) the same problem as you. The general answers to that would be "mech keyboard" and "practice". But how to practice with such slow fingers? I've always thought that if you play harder/faster maps your fingers will be faster someday, but it turned out to be false.
You should try maps like this one:
https://osu.ppy.sh/s/72474 (note: it's unranked)
It's just one (or two) long stream(s) per song. Use NF and HT, if necessary. I started out at 105 bpm (140 + HT) and improved to 128 (170 + HT) in a few days. I'd say I can stream at that bpm when I get about 500 combo, but that's always up to your own interpretation. When you play slightly too high bpm you'll find a way to somehow get faster with your fingers because you got the goal to hit the notes that are slightly too fast, but not out of reach.
I don't exactly know why, but the ability to reliably stream at about 130 bpm improved my streaming skills to such extent that I could easily stream 10-15 notes at about 160 bpm and stop dying at short 200 bpm streams.
So try it out. It's really boring, but the most effective way to improve it (at least in my experience).