Of/at this establishment

[A keen learner]

Dear all,

Could you please let me know if I can use the preposition "of" in the following sentence?

It's my first day at work, so I will do my very best to adapt quickly to the way of proceeding at/of this establishment.

 

[teechar]

the way of proceeding at/of this establishment.

The problem is not the choice of preposition. That entire chunk is unnatural.
Try:
It's my first day here, but I will do my best to adapt quickly to my/the new work environment.

 

[A keen learner]

Thank you very much, teechar .

I knew it sounded weird; that's why I've asked for guidance.

May I write then "It's my first day here, but I will do my best to adapt quickly to the work environment at/of XXX (a company name)"?

 

[teechar]

"at" is possible; "of" would be unnatural. If you insist on using the company name, then consider also:
"... adapt quickly to ABC's work environment".