I work for a big OG company as an mechanical engineer. Happy to talk to you about the ins and outs. You got an email?
In general, for a civil background its going to be tough to get a job designing tools and equipment for the large OFS companies. They can generally be picky and not have to accept varying degree tracks. If you want to do that, it might be easier to start with a smaller named outfit that'll allow that. If you want to actually go be a part of boots on the ground oilfield, OFS is the way to go. You'll make a ton of money, never be home, and have more time off than anyone else working a white collar job. The hard part about the field is leaving it and finding an office job. Most big OFS companies have a long backlog of people who want out of the field and not that many places to put them in offices. A lot of field guys just leave the company when the company isn't moving fast enough to bring them back into the office. Not all OFS jobs are the same. You've got drilling, casing, wireline, stimulation, servicing and overseeing surface equipment installation. Offshore, onshore, remote ops. Tons of ways to work nights weekends and holidays.
I do have a buddy who went civil undergrad, XOM out of undergrad, paid his dues in beaumont for 7+ years and then was able to move to the spring campus. Not the only way to spring but XOM is going to ask themselves why should they hire you and give you the suit and tie job when you don't know any part of the physical side of the company. You've got to pay your dues somewhere.
If you graduated last december, you can still try to apply to all of these companies through their new hire portals. Most large companies will take someone who has 3 or less years of experience and still happily throw them into the new hire program.