Well your filter isn't going to have a lot of bacteria due to your low stocking (3cm of fish!) And the plants will probably be dealing with most of it before it gets to the filter... that said the plants also provide a useful buffer too.
When I did a similar exercise, I managed to add about 40% to the stocking level each week without any detectable ammonia at any point (though I was also adding plants through this time). So you would be looking at adding just 1 fish at first, then 2, then you could add say 3 then the last 4 of that species. This doesn't really seem realistic here... I would probably add them in 5s but take things very carefully indeed after the first 5 are added and give it at least a couple of weeks for things to setle properly. You would need to be testing the water for ammonia and nitrite each morning and evening and be ready to change lots of water during this time if required if you detect either (especially ammonia).
If you get the youngest fish you can find they will obvs be smaller and so this would help. 3cm stocking (your neon) to 8cm stocking (adding 5x 1cm juvinilles) is much safer than 3cm to 13cm (adding 5x 2cm adults)! Furthermore, adding another 5cm (5x 1cm juvinilles) of stocking to 8cm stocking is far more reasonable than adding 10cm (5x 2cm adults) to 13cm stocking going by the percentage increases.