I suspect the true state of affairs is somewhat different from the suggestions here so far.
Firstly, I think that the Queen had already pledged to fund Andrew for as much as it would take to make it go away. And I think a conditional "decision tree" pair of scenarios was formulated and agreed by all parties within the Royal Family, well in advance of the judicial ruling last week.
I think that (rather obviously) Scenario 1 was if the judge threw out Giuffre's lawsuit in its entirety: I think that had that happened, the Queen would have covered all outstanding legal fees, and Andrew would - after a suitable waiting period of a couple of years or so - have been able to make a very limited return to public life.
And I think that Scenario 2 covered every other possibility (and note here that the judge didn't actually throw out Andrew's motion for dismissal last week - he merely ruled that this was the wrong point in the proceedings to assess the motion).
So..... whether the judge had thrown Andrew's motion out entirely last week, or whether he'd simply deferred a ruling on the motion (which is actually what happened), I think Scenario 2 went live in either case.
And Scenario 2 is "make this go away, as quietly and as quickly as possible, and the Queen will pay as much as it takes to make that happen". But the (pre-agreed) quid-pro-quo of this scenario was the cutting loose of Andrew (which is why that happened so quickly and brutally last week, hot on the heels of the judicial ruling: it had all been worked out, and agreed to by all parties, in advance).
My confident prediction is that within a month or so, Andrew will settle out of court (using the Queen's money), without any admission of culpability. It's worth noting at this point that when Giuffre's lawyer says things like "she wants her day in court" or "she wants the truth to come out".... this - more often than not - is simply posturing as a tactic to extract more money in an out-of-court settlement. Everyone has their price, and I cast-iron guarantee that there will be a sum of money that is sufficiently acceptable to Giuffre to engineer a no-fault OOC settlement.
It will almost certainly be a very large sum of money - maybe in the high two-figure millions. But I predict that the Queen, whose courtiers and bankers will probably have started on the financial engineering and asset liquidation months ago, will readily pony up in order to a) protect the image and reputation(!) of the Royal Family, and b) clear this thing off the table well before the Queen's Platinum Jubilee celebrations take place.
As I said, I think that the moment the judge didn't grant Andrew's motion to dismiss last week, a previously-arranged/agreed and well-choreographed process kicked in. And that all parties in the RF - including the Queen, Charles, William and Andrew - already knew the plan in advance: that Andrew would hand back his HRH and his patronages, and that the Queen would agree to pay whatever it took to settle out of court on a no-fault basis.