Thing is, for this you want to have a modern US fleet which is basically ALL composed of big, fast ships (otherwise, you get an indecisive engagement where one side's fast ships can open the range, and the other has to let them go or risk their own modern ships taking licks from the enemy slower ships as they go past)
This basically means nothing with a speed below 21 knots - as that's the fleet speed of everything Dreadnought and later.
And the RN fleet as of about 1916 included no fewer than thirty-seven of the things...
Assuming that things kick off in 1916. What does the USN have with a fleet speed of 21 knots?
The South Carolinas are too slow.
So that means everything Delaware and later.
Eleven, with three more building.
So.
Given that the Royal Navy has a demonstrated ability to churn out capital ships at a truly insane rate (I'm talking three or four a year, with an individual ship being in the slips for under two years except in extreme cases - many of them being in the slips for under one year!), the USN will have to go for parallel builds (i.e. more ships at a time) to overcome the RN serial build capability (more ships out of the same number of slips in the same time).
That's as far as I can tell you offhand or with a quick Wiki - more would mean looking at the numbers of capital ship slips both sides had active in (say) 1918. But it means the USN battle line has a disadvantage of twenty-three to make good, against an enemy that is not exactly standing still. (And I didn't even count battlecruisers (all of them with higher fleet speed; count is 8+1 nearly finished and four just started, BTW, and that's assuming Jutland has happened and three of them have exploded), and RN battlecruisers were themselves capital-sized in the first place.
Okay, I'm going to pull numbers directly out of my arse.
Assuming that the USN's construction rate is double that of the RN, year by year, so the RN commissions four new ships and the USN eight. (The RN could absorb that, albeit with some difficulty; the USN would probably have a major manpower crisis. But let's forget that.) Let's also assume that fleet speeds remain at 21 knots, and that armament is no more effective on later designs - or not enough to matter, except that the USN only has to outnumber the RN 1:0.7 in order to get the decisive victory.
So we want thirty-seven plus 4x to be 0.7 times 15 (generous) + 8x.
And based on these WAGs, the break-even point is in... 1932, when the USN's fleet of one hundred and forty-one dreadnoughts attains decisive superiority sufficient to force the RN battle line of one hundred and one to battle.
Clearly my WAGs are producing absurd results.
Okay, let's try again. This time, the USN merely has to exceed the RN's numbers by 10%.
Break even is 1923, when the RN fleet is 65 strong and the USN fleet is 71 strong.
What about if the RN doesn't build anything and the USN builds three ships a year?
1924-5 or so.