There's no physical restriction as to when you can post an official app. Remember, the app itself will be processed for at least two months of analysing the faction's performance. An app is there for when you want to go to officialdom, and what's required for officialdom is ingame presence, a good sense of RP, and a niche in the universe. DWR has all of these things.
Indeed, it's often advantageous to apply sooner whilst you have the impetus up, so when people start to get tired - boom, you're official and you can start crafting events, perks, and ID changes to keep people motivated by making your RP matter ingame and have some staying-power beyond just the members of your organisation.
For example, UN was a direct revive (same account even) of a faction that existed in 2015 as an official group, and that itself was a revive of a group from years before and used much of the same RP. UN had a leadership change (both InRPly and Oorply), and I took over during the officaldom application process (although at this point I was basically already steering the ship). I took Unioners to war with the Hessians as a means of proving that we could handle complex story developments - it indirectly helped get us approved, more likely than not.
Do audacious things as an UFL that exceed your abillity to implement as a UFL, then be active. Simply being active isn't really enough, you need to show that you can want to steer the entire NPC faction, rather than just log-and-trade, log-and-blue. There needs to be objectives, intrigue. Contrary to popular belief, story devs like it if you do their work for them.
If they do that over these two months (and they are, they're already crafting intrigue RP), I'd say yeah, knock it out of the park.
