Does a black hole have a ‘surface?’ If you had a suit that could somehow withstand a black hole, would it be possible to ‘stand’ on the singularity?
The closest that a black hole has to a surface is the event horizon, the location at which light can no longer escape, but this is not a solid surface that you can stand on. If you had a very powerful rocket, you could remain just above the event horizon, but your rocket would need to be infinitely powerful in order to "stand" on the event horizon and not fall in.
Inside the event horizon, not only can you not escape the black hole, but you cannot avoid reaching the singularity. No matter how strong your suit is, all parts of your suit will eventually hit the singularity, and so will be crushed. Jumping into a black hole is not the safest idea.