Wie sagt man das auf Englisch (US)? When I writer a letter to someone I don't know their sex,
which expression would be appropriate to begin with the letter in a polite way as I can not use 'Mr.' or 'Ms'?

Sehen Sie eine Übersetzung

writing a letter to someone is supposed to be personal, so you should know whether they are Mr./Ms./Mrs., otherwise the letter sounds very impersonal and generic.

If you are writing a generic company letter or a letter to provide information in general, then "to whom it may concern" would be fine.

If you're writing a casual letter, maybe to a penpal, you'd write "dear [first name]", but if you're writing a more formal letter, maybe with a business proposition, you want to use their last name. if you are unsure of their gender, and there is no way for you to find it out, you can always write "Dear Mr. or Ms. [last name]".