I would say that the forms starting with "To" are grammatical, but they are unusual in subject position.
I suggest that this is partly because there are other constructions which start a sentence with a "to" infinitive, that have a different structure, so you are likely to get a garden path sentence, which confuses the hearer.
The two constructions that occur to me are:
Purpose clause: "to be an engineer" is a common way of saying "in order to be an engineer".
Discursive: sometimes the effect of "I will consider your comments in order" is expressed by an initial infinitive clause: "To take your comments in order, ..."
Both of these actually have a different structure from your examples, and a hearer will eventually work out that you are not using one of them; but there may be a moment of confusion first.