Ammettere (to admit) is somewhat of a true cognate when used in the indicative.
We can use it when referring to gaining access, say, to a course or school.

Non è facile essere ammesso alla facoltà di medicina.
It’s not easy to get admitted to the pre-med program.

It also refers to acknowledging something, like an opinion or an error. Here, too, ammettere is a true cognate.

Ammetto di aver reagito troppo in fretta.
I admit I reacted too hastily.

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But, when we find ammettere with che (that), and it’s often in the past participle ammesso, it calls for the subjunctive, as Daniela mentions in a recent lesson on the subjunctive. But be careful because the meaning changes. Here it means “to assume” or “to suppose.” We are not confirming something, we are assuming. We're talking about something unsure, which is why the subjunctive is used.

Allora, un amico mi dice una cosa,

So, a friend tells me something,

io non sono sicura se è vero o no,

I'm not sure whether it's true or not,

e dico: "Ammesso che sia vero, è interessante".

and I say: “Assuming it's true, it is interesting.”

Captions 39-41, Corso di italiano con Daniela - Il congiuntivo

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Amettiamo che lui l'abbia uccisa.

Let's assume that he killed her.

Caption 38, Il Commissario Manara - S1EP10 - Un morto di troppo

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A common expression in Italian uses this form: Ammesso e non concesso (assuming, for the sake of argument).

Ammesso e non concesso che quest’uomo sia innocente, lui non avrà problemi a dire la verità.
Assuming, for the sake of argument, that this man is innocent, he won't have any trouble telling the truth.

or, more literally:

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Assuming, but not granting, that this man is innocent, he won't have any trouble telling the truth.

The verb assumere exists as well in Italian. But that’s another story, which we'll get to in a future lesson.