The Brazil winger joined from Ajax for an initial fee of £82.1m on Thursday making Antony the fourth most expensive signing in Premier League history, and the most expensive deadline day signing.
The 22-year-old put pen to paper on a contract that runs until 2027, with the option of an additional year.
Manchester United confirmed Antony will be added to squad against Arsenal but ten Hag kept his cards close to his chest.
"We have to see. Today he did his first training, individual, and then we have two team sessions and we will see for Sunday," he said after United's latest win over Leicester.
"Maybe that is too quick to say that (we have turned a corner), we are happy with it, that is sure.
"You can see there is raising a team, a squad raising, they are sticking together.
"They are supporting each other, they fight for each other, they cooperate - that is important - and if you do that you get the right scores and we did that the last three games.
"Now we have to step up further, we have to improve further. Sunday, a really good game, a really good test, so we are looking forward."
Ten Hag backed Jadon Sancho to become a prolific goalscorer after he sealed the 1-0 win victory over Leicester.
Sancho scored a fine effort in the victory against Liverpool and added a cool first-half goal in Thursday's 1-0 win against Leicester, with Ten Hag hopeful more are to come after the forward's difficult first season at United.
"I think he had quite a good pre-season," the Dutchman said.
"He understands now he has to invest in the physical (side) and that is what he did. Now he gets the reward and that is what he has to bring.
"I'm sure this is just the start for him. With his potential, there's much more room for improvement.
"Then he can be even more important and contribute with his creativity, with scoring goals and assists, and also with the defending part he can be even more important."
Asked if he believes Sancho can become a prolific goalscorer, Ten Hag said: "Yes, I think he can.
"He has the capabilities and he did it also in a different league, but this is the Premier League.
"The intensity is higher so he has to adapt to that, mentally, the physical (side). The capabilities are there, the skills."