Your first day is one thing. Someone else’s first day is another entirely.
On your first day, you only have to worry about the impression made by one person: you. On someone else’s first day, you have to worry about the impression made by everyone.
On your first day, you experience everything for the first time and are in control of your reaction. You manage someone else’s first experience of everything on thier first day and have zero control over how they react.
You present yourself as a competent professional who is worth the investment on your fist day. But you must present an entire organization on someone else’s first day so that they feel, right away, that working with you is worth their investment.
Someone else’s first day feels like a test of whether the work you’re doing is exciting to someone new. The rule surely applies here too: begin as you intend to continue.