Setting the initial value of a differential equation as an unknown parameter and to do optimization

I had a question about doing numerical fitting by ode45 solver and optimization tool. Is there a way to put the initial state as one of the fitting parameter and to find the best value from optimization?

I've tried with a known initial state value, z0, and the code worked well. The fitted line goes through the first data point designed as z0. However, I want to introduce more fitting parameters that the optimized curve might not pass through it.

Here is the original code:

ODE_Sol = ode45(@(t,z)MyodeFcn(t,z,c0), expTime, z0); 
simY = deval(ODE_Sol, expTime); 

myObjective = @(x) objFcn(x, expTime, expY,tSpan, z0);
bestc = lsqnonlin(myObjective, c0, lb, ub, options);

function dz = MyodeFcn(t, z, c)
dz = zeros(2,1);
dz(1)=-0.0356*z(1)-c(1)*z(1)*exp(-c(2)*t);
dz(2)= -z(2)*c(3)+c(1)*z(1)*exp(-c(2)*t);

I want to replace the known "z0" to [c(4) c(5)].