Very interesting, and something I wanted to do for a long time.
Do you know what is the main cause of friction? Your weight. The frictional force is usually a coefficient (less than 1) times the weight.
So this is a physics question I always had. If a person standing on a scale tenses his leg muscles to try to "increase" the force on the ground, will the scale show a higher reading? No.
I just tried it now and it is confirmed.
So, pressing against the ground cannot increase friction.
It can only provide a springboard to rise.