Delayed Initiative for 5e

So I have a potential mass combat coming up in my campaign. The way that I envision the session going is that when combat starts the entire map will be alerted due to a an alarm. The combat is going be taken in an underground base in the sewers, and as they progress from room to room, more and more combatants will be involved. I am looking for a way ( without scripts ) to make it more manageable. I understand that I can basically roll the initiative of each enemy every time the party comes across them, however I am concerned that having to add in the turns, reorder the turn order and then resort the order to the correct turn is going to be onerous and time consuming. I know that I could in theory move tokens to the GM Layer and roll their initiative which will keep their initiative hidden until I reveal them, but again, this requires a lot of moving tokens from layer to layer. The other option is to just mass roll all the initiatives to begin with however I feel it will basically give the scale of the battle without allowing the players to feel for it. I.e. its less immersive. I am probably butchering the explanation of what I want to do, but can anyone think of a way of getting around this?

If the additional combatants are only joining in as the players progress through the different rooms, why are they getting an initiative roll before then? If they aren't involved in the combat, they shouldn't have an initiative. The players also shouldn't be using the same initiative for different combat encounters. But, it's not really that hard to move an entire room of NPCs from the GM layer to the token layer, as you can select them all at once by drawing a box around them with the Select tool, then right click once and move them all to the token layer simultaneously.

Dakota H. said: If the additional combatants are only joining in as the players progress through the different rooms, why are they getting an initiative roll before then? If they aren't involved in the combat, they shouldn't have an initiative. The players also shouldn't be using the same initiative for different combat encounters. But, it's not really that hard to move an entire room of NPCs from the GM layer to the token layer, as you can select them all at once by drawing a box around them with the Select tool, then right click once and move them all to the token layer simultaneously. The point is, they will be involved. As I stated if the combat goes as I forsee then an alarm will be called alerting everything on the map. And yes I understand I can put things to GM and swap tokens between layers, but I am trying to find a way that limits that as it breaks up the narrative.

When combatants join the fight, do it at the top of the turn.  That way when you reorder the turn order you don’t miss anyone.  You could also roll a new initiative  at each phase of the combat.

If you have them on the GM Layer, you can make their initiative rolls ahead of time and sort the Turn Tracker. Players will not see them in the Turn Tracker until you move their token to the Objects and Token Layer. Alternately, you could declare their initiatives in batches of 3 (or 5 or whatever handy number), so one roll is for X number of NPCs.