What kind of monte carlo will you be using? Was it grown emersed or submerged, and is it a tissue culture or in a pot?
I just finished my 6-week dry start for a monte carlo carpet but I am going low tech, so no CO2. I was incredibly worried that my monte carlo would all melt like crazy, but surprisingly it didn't! Some did, of course, but most of it is fine and I'm almost two weeks in since I filled. And monte carlo is relatively easy to grow, and if you have CO2 then I would say you have an ever better chance of success!
If you are concerned about the rooting process, then I would say 2 weeks for a dry start is plenty for roots to start establishing in the substrate. Otherwise, you can just fill and go for it
The next thing you might consider is whether you want a full, finished carpet to start up your tank or you would rather start the tank as soon as possible and wait for the carpet to grow in over time.
I've heard that monte carlo grows at pretty much the same rate during a dry start as it does submerged with CO2, so I think it's mostly whether you want to save or expend the CO2 for a month or so while your carpet grows in?
And this is a very unverifiable hunch (lol), but I've read a bunch posts about monte carlo/dsm and the transition and I inadvertently noticed that tissue culture monte carlo seems to fare slightly better in the "transition" from dsm to filled than other types of monte carlo. I have no idea why, and I haven't seen anyone else mention it, so idk if it's true or not...but I also used tissue culture monte carlo and my transition went relatively well (so far). So that's just something possible to consider if you do decide to go with the dsm!