Concordium

So I am sure this question gets asked a lot. I apologize for that but searching the forums did not result in a clear answer for what I am trying to do. I have a 2019 Denali 1500 running on stock 20" wheels that are currently wrapped in 275/60 tires. I am wanting to get a 3-4" lift kit a little later this year. My third child is about to be born next month so I have been hoarding my money for that instead of truck mods. However, I just discovered that my tires are shot. I need to replace them as they are not really safe to drive on at all anymore. So I am forced to replace my tires before getting the lift......but I want to put on the biggest tires that will fit now but also be a good match for when I get the slight lift. I know absolutely nothing about the offsets for the stock 20" wheels I currently have nor how that impacts what tire sizes I can fit. Would it be better to stick with the 275/60's or am I able to fit a bigger tire without doing any cutting at all? If I can fit a bigger tire, what size would I be able to throw on? Thank you in advance for the assistance and suggestions.