The "nonce" is the random number stored in the coinbase transaction to change the block hash. If you mean the block hash (the thing that's targeted to be below a certain number) then that'll change: when a new transaction is added; when a transaction is removed; or when transactions are moved inside the block.

The mining software takes transactions from the mempool of the node running and organises them (they normally prioritise higher fees but could also prioritise their own transactions too ahead of that). Transactions are immediately minable once they're sent to the node and some mining software may shuffle round transactions anyway for finding the solution for the next block.