The both transactions being confirmed the same time is possible though the chances are also thin
Why do you think the chance is thin?
If the bot broadcasts the second transaction once it sees the first one and the fee rate used for the transactions are equal, there's a very big chance that both transactions will be included in the same block.
Two transactions can be included in the same block but will never be confirmed at exact same time in such a way it won't be distinguished. Even with both transactions in the same block the ordering will be visible to everyone onchain.
Thank you to all. Same block is what is needed, and indeed a larger fee seems to have worked in some cases I have seen.
Even with higher tx fee ordering will still be defined. There is nothing like exact same time inside a block, there is always a strict order recording for blocks in every Blockchain. The thing about validators is even with same tx fee and identical timestamps nodes will still put one transaction before the other. As far as miners are concerned there is no randomised order