The rules won't give the Warlock any explicit ways to achieve this. But the rules don't forbid this either.
While temporarily dismissed, you can't communicate with the familiar, as it would need to be pretty close:
While your familiar is within 100 feet of you, you can communicate with it telepathically.
but it's in a pocket dimension:
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons.
See this answer argument on how being on different planes (including a pocket dimension) blocks at least this kind of telepathic communication with a familiar.
The quasit's text about invisibility (the others have similar text) says:
Invisibility: The quasit magically turns Invisible until it attacks or uses Scare, or until its Concentration ends (as if concentrating on a spell). Any Equipment the quasit wears or carries is Invisible with it.
So no other relevant limitation, except requiring concentration.
If the familiar isn't already invisible, it will take at least and action to turn invisible after it is summoned. It will be at least briefly visible, if it was visible while dismissed. Even if you give it standing order to turn invisible when you summon it, it can't do it until it is its turn, which in the worst case lets everybody else in the encounter act first. Also, the rules don't give any choice to the familiar on when to appear. When you summon it, it appears on that turn of yours and can't delay it turn invisible first.
It should be possible for the Warlock to request the familiar to remain invisible while dismissed and waiting for summon, but it would have to happen while familiar is summoned. It needs to maintain concentration, so DM might impose some limitations to that (my ruling as a DM would be, that the Warlock would need to agree with the familiar on when it should be invisible while dismissed).