How to make a proxy without Nat?

Question

Computer networks

There is a network. The network has a gateway. Let's say the address is 10.10.10.1
All machines on the network have addresses in 10.10.10.0/24
The gateway is a "black box", that is, it is configured by a higher organization that distributes the Internet at the same time (unlimited).
Is it possible to somehow make a proxy on the border between the network and the "black gateway" without using nat?
There is an option - to make a web proxy, only for browsers. But those users who enter the default gateway address directly will be able to get past the web proxy. (I know it can be banned by politicians), but this will not solve the problem. There is software that does not know how to go through a web proxy, there are services that look inside the network from a higher organization.
The main task: how to direct all traffic from the network and to the network through one machine that can watch and filter it. (we don’t have smart hardware like ASA, from resources - only PC)

Answer 1

Something often with questions about proxies, not understanding how it works. If you read the wiki a little , you will see that proxy and nat are different things. And if there is no smart hardware, use software solutions - stick Linux or BSD on a PC, set it as a gateway, and filter, mask, proxy anything.

Answer 2

Put the router in the gap between the network and this device - configure everything you need on it, distribute your addressing and tydy. If there is no need for the networks of the higher device to go to you, then no one will notice anything at all.
A proxy will not save you in this situation.