Without joining a mining pool or broadcasting the transaction, wouldn't it be incredibly difficult to have a chance to successfully beat all the others and mine

Without joining a mining pool or broadcasting the transaction, wouldn't it be incredibly difficult to have a chance to successfully beat all the others and mine the block yourself? Or is the assumption that anyone who is able to solve the puzzle will also be able to mine any and all blocks instantly? And why couldn't you re-steal the award back again?