You are dealing with an idiomatic construction: "faire la rencontre de qqn".

(TLFi) Faire la rencontre de qqn, faire rencontre de qqn (vieilli ou littér.). Faire sa connaissance.
♦ Denise devint toute pâle quand ma mère me demanda si je n’avais pas fait rencontre d’une fille qui me plût et si je n’étais fiancé avec aucune (Lamart.,Tailleur pierre, 1851, p. 537).
♦ Le livre [L’Immoraliste] était tout composé dans ma tête et j’avais commencé de l’écrire lorsque je fis la rencontre de Nietzsche, qui m’a d’abord beaucoup gêné (Gide,Journal, 1927, p. 858).

It means "to meet someone". It is called a verbal locution (locution verbale).

An alternative translation, possibly preferable

• We thus meet the warm and often sleepy Santa Claus.

If you run that through DeepL you get your sentence; "rencontrer" is a synonym of "faire la rencontre de".

Hint: If you had checked the TLFi at the entry "rencontre" you would have got this information.

“Rencontrer” has a fairly large set of nuances of meaning, like “meet” in English. “Faire la rencontre de quelqu’un” specifically means to meet someone for the first time, and to get to know them at least a little.

“Nous rencontrons le Père Noël” could mean that we know him well, and we happened to see each other in the street and had a little chat. It could also mean that we got a brief glimpse of him, but he vanished quickly. Or it could mean that we met him for the first time, and we saw enough of him to see something about his personality, and possibly we interacted with him. With “Nous faisons la rencontre du Père Noël”, only the third interpretation is possible.