Donald Trump has indicated that the proposed USMCA means that Mexico would indirectly be paying for the wall many times over. What I don't understand is how, even if the trade is more beneficial to the US, this would be possible as I would expect that private employers would be the ones potentially benefiting from the deal.
No. The campaign promise that Mexico would "pay for the wall" was in a very direct sense, with the idea that his strong background in deal-making would be brought to bear in showing Mexico the benefit of either having a wall, from their perspective, or not angering the US.
A very oblique and indirect "we'll potentially have more money, and that pays for the wall" is pretty much in the realm of unicorns and fairy dust. How to measure the additional income, vs normal growth in economic activity from trade? And when a government that runs trillion dollar deficits gets a few million or billions more in income, unless the money is specifically identified and directed to "the wall" one could as easily claim it went towards Food Stamps/SNAP, education, a new tank, a trip to Mara Lago, towards deficit reduction, etc.
During the 2016 presidential election campaign, he very directly stated that the way Mexico would pay for the wall would be a "one time payment of $5 - $10 billion." He does make a reference to tariffs, but as a mechanism for forcing Mexico to pay for the wall, not as the wall-building revenue source.
He stated that this would be a direct remittance from them, and he was going to force their hands through the tariffs, blocking wire transfers of people sending money from the USA to Mexico, blocking visas, or by raising visa fees and using that fee increase to fund wall-building.
Basically, it's an empty claim aimed at saving face over his utter failure to get Mexico to buy in. It's standard Trump "moving the goal posts" in a pretty transparent manner.
Humorously, this utilizes the main arguments for trickle-down economics but is advocating for tariffs, something that is anathema to Reaganomics.
The argument usually goes like this: give the top echelon more money (in the form of reduced taxes) and it will 'flow down' to the bottom over time. And it's true, to a point. The problem is that for every echelon the money flows down, it is reduced by an order of magnitude. So giving rich guy $100 ends up giving middle-class guy $10, and poor guy $1. This is terribly inefficient and the math never works out as they say it will, at which point the argument goes to some abstract 'helping the economy as a whole', or 'a rising tide lifts all boats', without evidence.
The twist is that we are increasing taxes on both sides, making goods harder to buy and sell across the Mexico border, thus driving down the flow and demand of goods via that pathway in both directions. It's like burning down the house to kill a spider: you don't have a house, and have no idea if you killed the spider. It is a horribly inefficient way to achieve your goals, and more often than not, does the opposite of what you want to accomplish.
So in fact, the money we're getting from Mexico is decreasing from before Trump was president, making the wall more costly without actually contributing a cent.