Simon Cowell -- Daddy's Almost at the Hospital ... Keep Your Vagina Closed!

Simon Cowell's baby mama better tighten up her lady parts ... 'cause the "X-Factor" judge just landed in New York -- and he's making a beeline for the hospital.

We broke the story ... Lauren Silverman went into labor early Friday morning -- and Simon rushed home from London to be there -- but based on his look in the pic ... the soon to be dad doesn't look too worried about missing things.

Something tells us he won't be filming the gruesome process.