Not 100% sure about Java SDK, but JavaScript SDK allows to specify "now" as a cursor to be notified of payments happening starting from when this script runs.
Edit:
Looks like the method mentioned above doesn't work with Java SDK. The alternative approach requires two calls instead of one, but it was battle-tested and guaranteed to work.
Prepare request builder for transactions, set limit to 1 and execute it. Once you get the response, you have a paging_token for the first transaction in a list that can be specified as a cursor in streaming mode. If the first request returns zero rows, it means that there were no transactions on this account and you can safely omit a cursor in a streaming request call.