I received an initial Chat from a user I don’t know, how can I see their Profile?

When someone views your Profile from Discover People and then sends you an initial Chat message (Send Greeting), you receive a Chat message.
To see this user’s profile to learn more about them and to decide if you want to reply (which will make each of you a Connection for each other), you can tap on their Profile pic in the Chat screen or tap on their @username in the Chat thread.