Can buck converter increase current if voltage step down?
You have a 20V open / 3.5A short solar panal. Let's model that as an ideal 20V source with an interal series resistance of 20v/3.5A = 5.7 Ohm. The maximum external power you can draw from such a source is when the external load resistor is equal to the internal series resistance. This gives a current of 20V / ( 11.4Ohm ) = 1.75A. The external voltage is 10V, the external power is 17.5W.

The buck output you saw was 4.8V * 3.3A = 15.8W, so the converter was 90% effective. That is as good as you will get.

You problem isn't the wrong converter: you expect too much from your solar panel. Given the open voltage V and the short current I, the maximum power you can draw is 1/4 * V * I.