If I install a really old Bitcoin Core on old pc with Windows XP (offline), set the system clock to 2010, could it trick the software into generating the same address/private key as an early miner's wallet (e.g., one that mined 50 BTC in 2010 and lost his wallet

)?
Who else had that phishing sensitivity towards OP with his question being maliciously contaminated? Because it is assumed he is at all course trying to step on ones wallet which may have been disclosed to be an old wallet probably holding an attractive sum of Bitcoin in it.
Why would you even think of tricking the Blockchain with your PC and get revealed of a wallet seed phrase because with that intuition, you want to get access to the wallet trickily and not even that you are thriving to recover your lost wallet seed phrase.
Well that is a great work in the security mechanism of cryptographic as a Blockchain network because, you can not trick the network neither can you encode your PC to execute to break through and reveal others Privacies for you unless the rightful wallet owners device Privacies has been hijacked or the wallet security provider has been made vulnerable.
But if I must be kinda positive despites my skeptic thought, is the wallet you are referring to a custodian or non custodian wallet? Because if it is a non custodian wallet and you don't back the seed phrase and private keys up, there is absolutely no measure to have access to it but it it is a custodian, then you can use your contact address such as your email, phone number or whatever contact you may have used to backed it on the registration process to retrieve back your keys.