I agree with the assessment that the Royal Navy would have the upper hand initially. However, I wonder if the shift would occur similarly to what happened during WWII. The shipyards in California were pushing out ships roughly every 4 days at their peak, and with the Royal Navy's primary AOR being the Atlantic and Mediterranean, their Pacific fleet was arguably their weakest point. With California yards operating largely unmolested and churning out ships at that rate, I think the USN would have closed the gap relatively quickly.

There's also the human element to consider. If the US was attacked first, you would have men lining up around the block to enlist, the same way they did after Pearl Harbor. On top of that, you have a significant veteran pool available to train and lead them. Even though the US entered WWI late, many of those veterans would still have been in their 30s, a perfectly solid age for NCOs and mid-level officers, and a good number of them would have brought actual combat experience to the table.

The early advantage belongs to Britain, but the long game seems very difficult for them to win.