County-Level Estimate of 4-Year Olds by Race / Ethnicity

I'm working with a nonprofit that is trying to estimate what percentage of 4-year-olds they are serving in our county by race/ethncity, and I'm looking for the best denominator I can find. (Our county is about 400k people all together.) We need the number in the next few weeks ideally, so we can't wait for the 2020 Census numbers to be released by age and race in June (though we may update our estimates then). I realize that this is going to have a significant margin of error because it's a really small estimate, and we'd ideally like to have a sense of what the margin of error is. 

Of the ACS products, it looks like only the PUMS has the option to look at one-year age groups (even if that results in a crazy margin of error). But, it's my understanding that the ACS sample is weighted based on age, race, sex, and ethnicity. So, is using the ACS sample a valid way to get those estimates (since it only reflects demographic variables that are used to set weights)? And, would using the replicate weights to calculate an MOE / standard error (we typically use jacknife) actually give you an MOE / standard error (since the estimate is likely to be more sensitive to weighting than the sample)? 

We're also looking into using the CDC / NCHS Bridged-race population estimates, but they recommend against using the 1-year age groups at the county level. And, we wouldn't have any kind of idea of how much play is in that estimate. Our state demographer's office projects that our county's population of 4-year-olds (they provide total population estimates but not race/ethnicity) doesn't change very much. So, would using 5-year rolling estimates of the 4-year-old estimates be valid? 

I know that the estimates aren't going to be great either way (we'd just ideally like to know how not-great they are), but I'd be super grateful for any ideas or suggestions!