The process can be started any time, but you need to understand the steps it takes to get from seedling to bonsai. The obstacle here is that you probably don't yet understand what goes into working toward making a tree into a believable bonsai, or how open-ended your question is. That's not a slam at all, just an observation. My suggestion would be to join a club or start researching how to go about it while your tree(s) grow larger. It's not unusual to cut a tree many feet tall (10 ft +) back to a few inches from the ground, then train a sprout as the new leader, only to chop it back in similar fashion a number of times over several years to impart taper, which makes your tree look old and more in perspective to something in nature.

A first step on a trident maple center foreground and an oriental hornbeam left background:
{{gwi:12057}}

FWIW - not all tree species are valued equally as potential bonsai.

Al