Can I run 12/2 wiring from a load center to a junction box, then use 14/2 for branch circuits?
You may be miscalculating voltage drop
The first rule of voltage drop is: Calculate voltage drop based on the actual, normal circuit load, not breaker trip. Suppose you have 7A of lighting, but only 3A will be realistically on at one time, on a 15A trip. What number do you punch into the voltage drop calc?
3 amps. The normal load.
The second rule of voltage drop is: 3% is nonsense - nothing in Code even talks about this. 3.000% is super nonsense. Most of the voltage drop calculators online will consider 3.001% voltage drop to be condemning, and will force you into a larger wire size at that point. That is patently absurd. If the calc reveals a 3.5% drop, that is unquestionably fine. Larger drops are a judgment call, but they're your judgment call. Some loads these days are 100-264V voltage-flexible, so you can tolerate a LOT of drop, especially on a 240V circuit, which can be awesome for pole lights on farms. So suppose you are wiring a pole light that takes 100-240V. 120V voltage drop calculates at 7%. Is that OK?
If #12 is used in a 15A circuit, mark, mark, mark.
For instance now that Romex is color coded, bring about 2" of Romex jacket into the box, and overtape the visible yellow jacket with white tape - to make clear it is #14. Otherwise it will be too tempting to put a 20A breaker there. Mark the hot wire with a tag and write #14 wire on it.