Initial link outside subnet

Yes. 10.10.10.100 can directly connect to the 172.16.1.10 network as long as they are connected and routed properly.
But I did not get why you need 172.16.x.x network for the design?
You can use 10.10.10.x IP Range as well.

Ip not enough, I can only get one ip.

May you give some detail suggestion where and how to set the router, thanks.

First of all, if you can be clear on what you want to achieve, it will make things easy to explain.
Let us say that you have a router and two different networks, say 10.10.0.0/24 and 10.10.1.0/24.

So your Router needs one port to have a ip address of, say, 10.10.0.1 255.255.255.0 and another port with the address of 10.10.1.1 255.255.255.0.

Now both your networks are ready and you need to connect a switch and the clients to the router.

I can explain in details if you can explain the design.

If I set the big square as a router, then set 172.16.1.1 and 10.10.10.1 as 2 ip for the 2 interface with routing table ready.

But seems still not possible.

When 10.10.10.100 send out info and the target is 172.16.1.10, how will the package arrive there.

Thanks.