Electrical – Installing a 240V 30 A outlet for EV charging

To answer your biggest question: I'm pretty sure it's not code-legal to tap into the feed from your meter panel with split-bolt connections. It's possible that your breaker panel has some lugs near the bottom of the load side bus bars to connect a feed to a subpanel, but most don't.

So a possible solution is what Doxy suggests: a new 100A panel that feeds your existing panel as a sub-panel. Before you consider that, I'd check to see if your panel type admits half-size tandem breakers. These are breakers that fit two half-size breakers into the space for one normal breaker, and this would free enough space for a 40A breaker to your EV charging circuit in the garage.

Another possible difficulty, though, is that your 100A service is awfully marginal for the addition for a 40A EV charging circuit. Although you didn't give all the relevant details, I assume your 1000 sq ft house (does this include the basement, if there is one?) has an electric dryer. In my jurisdiction, a load calculation shows you would require a 107A service. You may be able to get away with a 100A service, but it will depend on your inspector/permitting authority.

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.