There are 4,294,967,296 possibilities in 4 bytes.

To store a number in range of 0 to 4,294,967,296 - you will need exactly 4 bytes.

Not all 32bit sequences can be found in the first 4,294,967,296 binary digits of pi. Hence you will either need more then 4 bytes to encode 4 bytes in a pi position or a lookup table to fit the 4,294,967,296 numbers, some of which will be substantially larger than 4,294,967,296, into 4,294,967,296 slots.

To save us from searching in the number space after 4.3-ish billionth slot, we could just store the sequences that we didn't find in that part of pi. I propose a bit used to indicate whether the current sequence is a pi-sequence or just raw data.