Can I generate an address without using bitcoin core?
Bitcoin Core does not store the information for all addresses as that would be computationally expensive and not very useful. For you to get this data, the address needs to be part of your wallet. So you must add the address to the wallet using importaddress and allow Bitcoin Core to rescan the blockchain. It will then find all of the transactions related to that address and look for new transactions related to that address. Note that rescanning can take a long time so if you want to import multiple addresses, use importmulti.