The PM should not be making estimates for anything other than the work associated with managing the project. Instead, the PM should collate estimates from the team members for the work that they will do.
In addition, think about why you have a budget. I would argue that the most important function it fulfills is to help give you a justifiable business case for proceeding with the project. In that sense you need a more holistic idea of costs beyond work done on the project, you also need an estimate of likely ongoing costs once the project products are delivered.
That being said, the budget for project work generally covers:
- Subcontracts. This is relatively easy, use the cost quoted by the subcontractor chosen.
- Labor. Get this from the team leaders delivering a work package. Use your company rules to convert full-time equivalents into $ terms.
- Materials. Again, get this from team leaders delivering a work package.
- Risk. You should allocate money to deal with risks should they occur, but this should be a separate "pot" and not used unless the risk the money is earmarked for occurs.
Post-project ongoing costs can be broken down into similar buckets, but should be kept separate from project work costs.
Regardless of the budget that you come up with at the start of the project, it is an estimate and will likely have to be revised as new information comes to light.