Same computation order using postfix notation?

I’m trying to understand arithmetic using stacks. Specifically converting infix notation to postfix notation. My question is how you convert an expression like: 1 + (2 + 3) + (4 + 5) that computes in the exact order that the order of operations says.

Meaning: 1 + (2 + 3) + (4 + 5) becomes 1 + 5 + (4 + 5) then 1 + 5 + 9 then 6 + 9

If you do:

Push 1, Push 2, Push 3, Add, Push 4, Push 5, Add

Where Add pops the top two operands off the stack, adds them, and then pushes the sum back on the stack.

Alternative notation: 1 2 3 + 4 5 +

How do you add 1 + (sum of 2 and 3) next? If you do another Add then the sum of 2 and 3 will be added to sum of 4 and 5, because these are the top two on the stack. Is it impossible to do it in the exact same order? Doing each parentheses group first left to right then doing the rest of the computation left to right.