To answer your question- Yes you can. It's perfectly sound.
You end up transposing to a Botvinnik system in the English Opening at some point.
This is fine, but it's very slow, very closed, and may not be what you want out of your openings if you play e4. As suggested, your good variation choices go as follows:
1. Some Open Sicilian line- If you dislike 1.....
There are lots of variants in the Sicilian that will fit into your game, just study them and find one you feel comfortable with. Sicilian is probably the most studied defense in chess, there's room for everyone
You can, but if you like most openings with 1.e4, it's probably not the most adequate choice for your "style" (the resulting position will be "slow" rather than a fast exchange of tactical blows. 2.c4 is a legitimate option, but here are a few alternatives you may want to consider:
Find some line in the Open Sicilian: this is the ideal, but requires a lot ...
It is not the most ambitious choice, but should be playable. It has been played by 2500 rated players. Basically by playing c4 you weaken your dark squares and black could try to take advantage of it by the following set up.
1.e4 c5 2.c4 Nc6 3.Nc3 g6 4.g3 Bg7 5.Bg2 e6 6.Nge2 Nge7 7.d3 O-O
If you are fine with such position go for it. I wouldn't ...