The starting price is the starting price - so in fact it is unknowable until after any race has in fact started; it is the last price for each horse at which decent money was laid just before the off.
The market is dynamic before that point, and in a constant state of flux, so the best that can be achieved in terms of "knowing" the starting price in advance is an estimation. That estimation will of course be more accurate the closer to the race time off that any prices are collected. The Betfair API is probably your best option for grabbing back prices just before any race; however, that itself is a different system to the starting price mechanism - a comparison of these prices and more is covered in this blog piece which may be informative, and also discusses the value of forecast prices in the Smartform database and betfair early prices (which are included with the Betwise oddslines):
https://blog.betwise.net/2019/07/08/bookmaker-vs-betfair-odds-comparison/