Not good news unfortunately
Having recently retired after 40 years as a Licenced Engineer B2 and C cat, the only advice I can offer is to try and get practical experience, even if its unpaid work !
Here in UK there are hundreds of 'enthusiasts' who have effectively undermined the employment prospects of genuine aircraft mechanics by working for nothing - usually in small GA outfits or on restoration projects.
Unfortunately the industry in general has a dislike of 'graduates'. I can recall some with a poor 'work ethic' and others so hamfisted I wouldn't let them near a bicycle, let alone an aircraft - yet they had glowing uni references and degrees !
A grad can get employment with large companies however, usually in the fields of planning and maint control - these are desk jobs and the starting salaries are poor due to the need to 'prove oneself' initially to the employer and too many people chasing too few jobs. However, stick at it and in a few years you might earn decent money.
I was an indentured apprentice (5 years) and learned 'on the job' along with day release to a technical college for the theory side. This got me City & Guilds certificates which at that time allowed me to bypass some of the theory papers on the old ARB (CAA) licensing route.
If you want to earn decent money working on aircraft in a practical way then a licence is essential - unfortunately the graduate route doesn't cut it with most employers.
However I don't envy anyone starting out from scratch on the current EASA licensing procedure - give me the old ARB and CAA any day !