First Pilsner, Lagering Question

I just brewed my first lager on the 4th. Pilsner with hallertau hops during the boil then a touch of nelson at whirlpool. It’s currently fermenting in the low 50’s then I plan to slowly raise the temp up for a diacetyl rest.

My question is after that’s done, I plan to transfer it to a keg to lager for 6-8 weeks at 35°, (not trying to rush the lagering process) can I start carbing the beer while it’s lagering or do I wait the 6-8 weeks before I hit it with co2?

I usually hit my lagers with some CO2 to flush out the oxygen from the keg but hold off on actually carbing. I don’t have a scientific article to back up my claim at my disposal right now but from my experience of traditional lagers fermenter pressure is actually the enemy here. The best lagers I’ve ever had were open fermented and cask-lagered. I normally just hook up CO2 at serving pressure at the last week of planned lagering and serve.