Make sourdough starter without discarding
While I have successfully begun a starter with only 10 grams of flour at the outset, I think I agree with Stephie that doing a little more is more efficient.  I used to do very wasteful starters until I happened upon this site back in 2002 or something.  (Amazingly, it's still there.)  You can read the details there, but basically the guy who did it designed his initial starter regimen based on the amount of flour he'd eventually use to bake bread (i.e., with no waste).  (It also has a way to get to a lower pH earlier which helps the starter along while inhibiting bad stuff; this was years before the internet discovered the "pineapple juice solution.")

But I think this depends a LOT more on your feeding regimen, especially in the early days, as well as the flour.  I've written a lot about the variables in my other answers here on sourdough related questions, so I'm not going to repeat it all here.

Briefly, though, YES, it is possible.  It can be just as reliable as using more flour and a lot less wasteful.  Even if you don't do a true exponential growth model for your starter, you can also be significantly less wasteful by keeping the starter relatively small until it's established.  There's no reason to be feeding and throwing away a cup or more of flour every time for every feeding, particularly if the starter isn't even growing yet.

Also, the same applies to maintaining your starter.  If you want to do detailed calculations, I've explained them here.  When I first started with sourdough, I used to produce way too much of it and throw it away.  Now I generally save just a tablespoon or two, feed it a little, and put it away for the next batch and build up from there when necessary.