You have to adopt him and the chances of a plebeian getting the consular trait are almost nil though. You need a lot of influence and quite a bit of command to be a consul. I am sure you have generals with better command and influence, and so the office of consul is going to go to them, not your Libyan General.
I have plenty of adopted Client Rulers as well as Mercenary Generals and most of them have ten influence with about 3-5 management and 2 command on average but only two of my adoptees held any public offices. My most notable one, a 6 command, 10 influence and management started out as a Mercenary Italic General with a couple of negative traits as well as with Plebeian, Dull/Charismatic/Vigorous, Unselfish/Pessimistic(!)/Loyal base traits. By now he is a Plebeian Tribune, Plebeian Aedile, Censor, Aedile, Praetor, Quaestor. He is also nobile and a member of the eques (he also has the very wealthy trait). And it has been only 5 years since I have adopted him! I'll have to see if he becomes a Consul - that will be a pleasant surprise for a dull, mercenary general, plebeian!
Do you really lack anyone better than the Libyan general? You have a general that you start out with that has sharp/charismatic/vigorous - Lucius Cornelius Scipio. if you put him in a city with Temple of Ceres, he has a good chance of getting the Popularis trait and if you send him off to battles he will get enough influence and command to be a consul. Then he could be the reformator. In my ongoing romani campaign, he's my reformator actually.
EDIT: MAA beat me to the posting, but he's right - you have to be a family member to attain the offices. You'll have to send the Libyan general into field battle and hope that you have enough territories (its actually the territories : FMs ratio, according to which you have one FM per 2.5 territories) to trigger an adoption request.
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