it is very possible you can make $100 in 2-3 months, there are a lot of activities you can do online e.g signature campaign, selling of skills like programming ,graphic design,trading e.t.c. the most important thing is to remain focus and devout your time toward it, i.e be dedicated toward it
Being honest since he does not have any capital in hand he really cannot make any significant amount unless he has a special hidden talent and as he asked that is $100 possible with a $20 investment ..
I would say NO, at least not at all safely, you can invest all your coins in a shitcoin and hope it grows but the chances are low always.
While you can on the other hand trade bitcoin's price and earn but that is kinda slow