Job application - no closing date but now it's closed, I still want to apply...

[PuppyPerson]

I saw a job on Weds eve that I liked the look of, it didn't have a closing date/deadline for applications.
Crazy busy week but planned to apply this weekend.
I looked last night and it's now closed for applications.
I'd like to still try, I can put an application together answering the standard questions (same questions and CV/cover letter upload for all of their open jobs).
What I would love help with is how to phrase the accompanying message/ email?
Is "I see it is now closed but I'm hoping you might still consider my application" enough?
I think I'd need to be a bit more apologetic if there was a deadline I'd obviously missed, but I didn't know when it would close 🤔.
Or should I just not bother because it's closed?
Any advice much appreciated!

Can't hurt to give it a go- I applied for a job recently just after the first deadline (there were 2 deadlines and interviews were going to be in two groups for first and second deadline people) and yet my application was put in with the people who had applied before the deadline- depends on the person dealing.

I'd try to phrase it in a way that makes it sound as if you just saw the ad rather than you saw it but waited. Be prepared not to hear back though.

Usually happens when they have received lots of applicants. Too many to continue to screen.

No harm in trying. Think your phrasing is good. Just don't be too disappointed if you don't hear anything, it might be that they've been inundated, or have been able to fill the place internally. Worth asking for your name to be kept on file for any future opportunities in any case. Good luck!

Thanks! I've applied to a handful over the last year or so without any luck so I am used to not hearing back anything at all even if I do apply before it closes! But I'll give it a go. I do find it annoying when there's no closing date though, as it means you have to drop everything and rush something in which may have been a better application if you'd been able to give it more time. Anyway, hey ho. It seems to be the way these days. At least this one included salary information!