Let us take the simple case, we see the iron spectrum of a star shifted, and we can use energy conservation to assign a velocity to the star that would assure the Doppler shift of the spectrum.
The expansion of space was deduced because a redshift was measured that can only be interpreted as "every cluster of galaxies is moving away from every other cluster of galaxies ". This led to an image of an "explosion", i.e. the original Big Bang model. In an explosion energy conservation comes considering the whole system, original energy transferred to parts. The complication comes from General Relativity which does not have energy conservation as part of its structure. It is only in flat spaces where Lorenz transformations can be effectively applied , as in the case of a receding star and the spectrum of iron, that one can talk of conservation of energy.
So,imo, qualitatively energy in all its forms comes from the original Big Bang, but one cannot write down general conservation of energy equations, they have to be compatible with general relativity.