Hey there! Im developing a Data Reconciliation routine.
I am applying a convex first part, that provides an initial solution, and ideally, that solution can be used as an initialisation for a non-convex second part. Is there a way to do this without writing in two different instances of gams?

Your question is a little bit too general, but I would say that this is just solving your model, and if the second part has the same variables, no initialization is needed and just solve the second one after the first solve.
If the second part has other variables that should use the solution of the first part as an initialization, you just initialize them (e.g,X_second.L = Y_first.L + Z_first.L).