Is the STAKE even obtainable in a first NG+ run?

I've beat the game twice (once at launch, once when 3rd person and Shadows of Rose dropped). I opted to not do NG+ cause I wanted to go through the same progression as a standard run again. But now I'm finally doing NG+ as part of my RE marathon leading up to RE9. I want the STAKE but I dont have anywhere near enough Lei. I have like 30,000 and I need 300,000 💀 obviously maxing it out for infinite ammo is just not on the table for this playthrough but is it even possible to obtain it to begin with on a first NG+?