#Mathematica, 42 39 bytes

N[Log[-(d=I/I)]/I,((c=d+d)^c^c^c)^c-d]&

Output Returns exactly 4294967295 digits as requested.

If more digits were allowed, then by outputting 7.76e17 digits (if even possible lol), 26 bytes would be possible:

N[Log[-E/E]/I,E^(E^E*E)]&

###Sorry but Pi = Ln(-1)/i.

Mathematica, 42 39 bytes

N[Log[-(d=I/I)]/I,((c=d+d)^c^c^c)^c-d]&

Output Returns exactly 4294967295 digits as requested.

If more digits were allowed, then by outputting 7.76e17 digits (if even possible lol), 26 bytes would be possible:

N[Log[-E/E]/I,E^(E^E*E)]&

Sorry but Pi = Ln(-1)/i.

#Mathematica, 7.76e17 digits (if even possible lol), 26 bytes

N[Log[-E/E]/I,E^(E^E*E)]&

###Sorry but Pi = Ln(-1)/i.

#Mathematica, 42 39 bytes

N[Log[-(d=I/I)]/I,((c=d+d)^c^c^c)^c-d]&

Output Returns exactly 4294967295 digits as requested.

If more digits were allowed, then by outputting 7.76e17 digits (if even possible lol), 26 bytes would be possible:

N[Log[-E/E]/I,E^(E^E*E)]&

###Sorry but Pi = Ln(-1)/i.