How to identify peaks in overlapped data?

I am trying to fit a model to experimental data shown below (blue - experimental, green - attempted fit). My approach has been to use lsqcurvefit() and specify a starting point for the algorithm. The fits I am achieving are nowhere near close to the original data and I think it is because of the starting points. Is there a way to identify the 'hidden' peaks in the data? I tried to use the curve fitting toolbox however this only goes up to an 8th order Gaussian and doesn't produce a satisfactory fit (screenshot shown below). I have tried to look into how the curve fitting toolbox calculates its starting points but had no luck, is there a way to use the curve fitting toolbox for higher order fits?

Thank you.