I feel this is as close to “Management 101” as it gets, or even “employee-ing 101”, as it applies to technical roles too.
Don’t do it!
Just write down your list of gripes for the first month; use them as your list of things to ramp up on.
If something seems odd or wrong, it may be actually broken, but it’s unlikely to be so urgent that you have to go out on a limb like this.
It’s more likely that there is some context you are missing. By Chesterton’s Fence you need to spend some energy to understand why the thing was put there, before you tear it down.
Even if you are right - you will face an uphill battle because you haven’t built trust yet. So pick your battles carefully!