The only option for him is to return to Mexico and you file a petition K1 visa to have him re-enter LEGALLY and marry him within 90 days of his re-entry, then file I-485 adjustment of status.
The fact that he came in the USA ILLEGALLY is grounds for him to be deported, he should NOT be granted any immigration benefits or privilaiges, As far as ICE/ USCIS is concerned his first act on USA soil was a federal criminal act of defiance in no way would he be granted GC or any other benefits & shouldnt be!
Its not too late for him to go back to Mexico and enter legally, if he does not and later is found out to have entered illegally he will be banned for 5 + years. If he really loves you, & you really love him encourage him to go about the process legally!
Its the only way.
Sorry to be so blunt but it is the rigt way and only way you and he will be able to enjoy a Happy legitimate life together in The USA.
Best wishes & I sincerily hope this works out for you both.