Below is suggested wording—feel free to personalize and edit—to introduce yourselves to the customer.

Remember, "the thing about first impressions is that you only get one." The customer has not met you, heard of you, seen your picture, or anything else. Thus the entirety of their initial impression of you will be shaped by what you write. Be polite, but not sycophantic or servile (look it up); you and the customer should be treating each other as professional peers, so your communication should establish that tone.

Advice for the letter and followup communications:

For title, it's best to start by addressing the customer more formally as Mr. or Ms. ----. If you know specifically that they have another title such as Prof. or Dr., it's a nice courtesy to use it, but in most cases you won't know, so Mr./Ms. is acceptable.
Scheduling is hard! The customer may indicate a particular time is free, but if you wait before confirming that time, it may get scheduled. Consequently, when the customer replies to your scheduling request, give it your immediate attention. After Iteration 0, if it's possible to schedule a regular recurring meeting time, that is best.
Use a standard video-conferencing tool that the customer easily has access to (e.g. Zoom) and won't need to install any new software to use. If you have access to/prefer another tool, that's fine, but don't make the customer install software just to talk to you.
Unless there is no other choice, don't settle for a voice-only call. A lot is lost in the conversation and you will miss the opportunity to establish a more trusting relationship with the customer.
The designated contact team member (see letter) should be the one who sends the email, cc'd to all other team members. That way if customer just hits Reply it goes to the correct person.

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Dear <title>:

We are the student team who will be working on your software project <project name> this semester, as part of our Software Engineering course at UC Berkeley.

We are excited to have the opportunity to work with you [or with you and your firm, organization, etc] and our goal is for you to be pleased with both the end product and the experience of working with us to develop it.

As a first step, we would like to schedule an informal meeting with you of about one hour to learn more about your business need and some specifics of the application and its features. In this first meeting we hope to learn enough about your business that we are familiar with the terms and language we will be using together to collaboratively design this app. We will then schedule follow-up meetings with you to discuss specific features and how you'd like them to work.

We are available to meet at any of the following times: [specify your times, or use a Doodle or similar poll]. Please let us know at your earliest convenience about a meeting time, and feel free to include any questions you have regarding this process. To keep things streamlined for you, <team member name> will serve as the primary communication contact. Thank you and we look forward to meeting and working with you!

Respectfully,

Contact team member: <name, email, phone/SMS, Skype or other ways to reach you>