Jumping in here as a fellow beginner who's about 3 months "ahead" with learning about the seedling process and Delonix regia specifically. I say that in terms of time, not necessarily knowledge
although have been doing a fair amount of horticultural reading that's hopefully not a total waste. At the moment, I'm managing ~50 seedlings that are ~3 months old, in standard 3" plastic nursery containers. I also have another 50 month-old plants that are in Rootmaker containers I received for Xmas.
I start fertilizing after the second set of true leaves (not the cotyledons) emerge, using Miracle-Gro "Quick Start" per directions (apply again 7 days later, wait another week and then begin with a 'standard' fertilizer program). This seems to work well enough, but I plan to run mini-experiments on different regimens for my next batch of seedlings in March. Since a major mistake I made was starting the seeds at the wrong time of year (fall/winter), which has mostly kept them under lights and not receiving the benefit of full sun. I'd started a few trays of Austrian Pine and Siberian Elm and soon gave up on all but a couple; I understand from others (Leo) that such species in particular need to be timed right, so will attempt them again in March. I just caught the bonsai bug bad this fall and couldn't wait to start SOMETHING; Delonix regia's no pre-treatment requirement fit the bill for me and perhaps it was similar for you.
The attached photos were all sown in mid-September (have a few others not pictured), just so you have a sense of four months of (weak) growth. I find them to be VERY sensitive to mis-watering (under- but especially over-), where the leaves turn yellow and/or drop off entirely. So depending on the soil media that you're using, be mindful of the difference between 'moist' and 'wet' and certainly poke holes in the current container or transplant it ASAP. The one that looks the best right now had looked like the others just a few weeks ago, so they can recover and don't be discouraged if (likely when) it happens to yours. I've started hardening these off outside when the daytime weather is > 55F, although think it got too windy on a few days and will be too cold next week so that transition is set back; no idea how much growth to expect under full-sun conditions.
I look forward to seeing how yours progress, will try to make more mistakes in advance so you don't have to