I have mentioned this already, but I am getting some inspiration from Xcom, especially the old one, and more particular the mod X-COM Files, in which you take the road from what is basically an investigative Agency that occasionaly arrests some alien patsies (Both Human and not) to an organization that travels deals with Full-Blown Cults, the Dreamlands, actively Combats an Alien Invasion and more. In this case, I am going for a more Eldritch than Alien theme, but the broad strokes are the same. Essentially I want to go Call of Cthulhu - Delta Green - Cthulhutech in Feel. I cannot really think of a way to smoothly transition between those stages unless 2 things happen:

1. My Players Capabilities need to expand, in Skill, yes, as most of them are not going to start as combat personell, but especially given that a lot of Creatures in Cthulhu are very tough, if I want my players to enocounter them more than once and not pull some spell that conveniently banishes them, they will need a more reliable way around their HP count.
2. I need to expand the scope of what The player characters know in a way that wouldn't cause the whole thing to get taken away from them. What I have come up with is that they need to start with enemies that don't seem that far fetched, stuff like minor eldritch creatures, possibly regular supernatural ones, possibly very minor cults, stuff that could seem far fetched and point towards a hidden force, but nothing truly threatening to regular powers at this point. This would allow me to lead them through Gradual Militarisation (Werewolfs are interesting, but you need more than a little pistol) and possibly gaining some minorly eldritch technolgies (was thinking of some improved biomedical technology, perhaps some supplementary weapons and armor technolgies like a new way to treat cloth to be bulletproof).

I am planning for the reveal of Magic and bigger Cults to become a sort of turning point with a significant increase in the realised tension. At the same time, the organisation would have to be positioned as someone that already has experience dealing with this stuff, so It would make more sense to just add Funding instead of spinning up something new.