Got the Alpha Skip Invite. Check your inboxes for those who applied!

You dont apply for skip ahead you get invites

Alpha is application

There is only a limited number of free slots in Alpha/Alpha Skip Ahead.

If someone in Alpha/Alpha Skip Ahead leaves, or is removed due to inactivity, participants in Beta are invited to Alpha. However, Beta participant invitations are sent out to those, that leave valuable feedback, find bugs, and are most active in the beta
group.

So it's not how long you are in the program, but how valuable your input and bug reporting was in the past.

Added to the fact that invitations are only sent out if there is new room in Alpha, you might have to wait a while to get invited. Just provide good feedback and be patient.

That's not how it works. You can move up in rings based on your activity in the program. Alpha and Alpha Skip-Ahead is by invite only, but those invites are sent by Microsoft. There's no way to ask for an invite. https://support.xbox.com/xbox-one/console/xbox-insider-program

You must be invited to become an Alpha Insider or Alpha Skip Ahead Insider, to do so You must Very active in Xbox, doing missions and report the bugs You see in the system, as much as You do this, so You Will be Very close to become an Alpha Insider. You
must be at least in Delta preview to become an Alpha Insider, but You Just need to be an Insider to be invited to become an Alpha Skip Ahead, but this one is very rare to be invited and there is a certain number of people to be invited, no more than that,
If You were not invited to be Alpha Skip Ahead certain time, so You must wait a Second chance when they Will invite New members.

You don't unless you join the insiders program which is on alpha skip and alpha only

Which both are invite only