The Black Cats have made an inauspicious start after picking up just two points from their opening four games prior to thrashing Stoke last time out.
Sunderland's slow start following a summer overhaul has led to question marks over Bruce's future, talk Bramble thinks is 'crazy'.
He is well aware rivals Newcastle sacked the late Sir Bobby Robson in August 2004, a move which brought few dividends.
The Stadium of Light side have made a number of signings during the close season and Bramble knows the new faces need time to settle, urging chairman Niall Quinn to keep faith with Bruce.
"I think Newcastle's downfall was Sir Bobby leaving," commented Bramble.
"It came from nowhere really, four games into the season. You make your signings and then you sack the manager - it's crazy.
"We've got ten new signings, so it's not going to happen overnight. It takes a few weeks, a few months for everything to gel, so four games is crazy to think about sacking a manager.
"Even last season, when we lost a lot of games at the back end, maybe a lot of clubs would be thinking, 'Right, let's get rid of the manager'. But it doesn't do anything.
"It's great that we've got a good chairman who knows the club inside out and who knows that changing the manager wouldn't do anything."