Can I come off the meter box to add a 60 amp subpanel
Yes you can...

Your configuration is anticipated by NEC 230.40 Exception 3:


  Exception No.3: A single-family dwelling unit and its
  accessory structures shall be permitted to have one set of
  service-entrance conductors run to each from a single service drop, set of overhead service conductors, set of underground service conductors, or service lateral.


but you're making your life harder than it needs to be

Your problem, though, will be jamming that outsized URD cable down the conduit.  It has one more wire in it than you need (since you haven't hit a service disconnecting means yet, you don't need to separate ground from neutral for this run, and the panel in the garage will be a main panel), and running cables through conduits is a pain in the rump as a general rule, in addition to being rather wasteful of conduit fill.

Instead, I'd suggest running a trio of #6 copper THHN/THWNs (black, black, white) through a fat conduit (2" Schedule 80 PVC is what I'd use in your shoes).  This makes upgrading to a bigger service to the garage easy (compared to digging up a direct bury cable or pulling wires out of an overstuffed conduit), and also won't leave you tearing your hair out trying to get a reliable termination on AA-1350 (yes, URD is still "old tech" aluminum) wires.

Last but not least

Since you are running to a separate structure, you'll need to put in a grounding electrode system at the garage (2 rods 8' apart, with 6AWG bare copper going rod-rod-panel, always works).  This is needed to make sure that a nearby lightning strike doesn't completely fry the contents of the garage.