re: "What would be the best way to proceed further?"
You worked without a contract. You can't get paid. If the client paid you - without a contract in place - then you would be violating serious Upwork rules. You could be suspended or removed from the platform.
Learn from your mistakes. Don't make those same mistakes again in the future.
Do not try to get paid for this task. Remove all desire to get paid for this. Never again send messages to that client.
The client needs to send you a contract, not the other way around. He responds to your proposal by hitting "Hire Now". It's not hard to figure out on the client side. He may be truly clueless, and you could remind him he needs to open the contract and not the other way around, but likely he was preying on the fact that you are new and haven't read up on how to use Upwork yet.
It's also a TOS violation to communicate outside Upwork prior to having a contract in Upwork. You need to read the help articles to make sure you don't get scammed, like you probably did here.
I am sorry to hear about your experience. Could you please click on my picture next to this post and send me a private message with more information on the client so I could forward this to the appropriate team to review and take action?