can you build your own support beam
You need to discuss in advance with the engineer what your plans are. In virtually every case I have ever looked at, it is possible to design a wide variety of different types of beams that will function, at different cost points and with different pros and cons.
For example, it is often possible to spec either a steel beam, nailed up wooden beam, Glulam, Microlam, LVL, flitch beam, or truss. If you are dead set on building this beam yourself, discuss this with the engineer, and ask them to design a beam that you can build yourself.