Is there any way that the time on the BTC transaction is wrong? (I mean at 20:42 I was not home). But it's that 20:42 my actual time?
No one can tell for sure when the transaction was first broadcast. The time you see on blockexplorers is the block timestamp (when the block was mined) not the time when the transaction got broadcast.
Blockchain.com says the transaction was first seen 30 minutes earlier which might be accurate given the fee rate that has been set which is more than enough for a fast confirmation at that time.
The most likely scenario is that someone got access to your wallet seed and used it to restore the wallet and move the coins. Only you can figure out how this happened.
Sorry for your loss!