I have never heard of anyone using EVPL for a branch network of this scale. This sounds unusual.
EVPL is a point to point Ethernet service. So you will probably have a VLAN per site presented to the data centre. You will want a layer 3 switch that can support a large number of MAC addresses. You would create a layer 3 interface per site on your core switch. I would consider an MS350, MS410 or MS425 series switch. Of course, you really should have a pair for redundancy (and form a stack).
Note I have never tried creating 100 layer 3 interfaces on Meraki switches before. You would need to verify with your local Meraki rep what the maximum number of layer 3 interfaces are supported on the model of switch you end up going for.
Now that still leaves the branches. You could plug the EVPL into a layer 2 switch. This will limit you to a single VLAN at each site. All traffic will be bridged over the EVPL back to the layer 3 interfaces on the core MS350/MS410/MS425 switches. Suitable switches might be the MS120 or MS210 series.
Another option would be instead of having the layer 3 default gateway of each site back at the DC, to instead using a layer 3 switch at each branch, and do the default gateway processing there. Then just use the EVPL network as a "stub" to connect back to the core network. At 100 sites you would want to be using OSPF, which means you would need a minimum of an MS250 switch (lowest end switch with OSPF support). Having a local layer 3 switch would also allow you to create multiple networks at each branch (for example, data, voip, guest, etc). However the solution may now cost more than putting in an MX ...
This now gets all your branch traffic back to the DC. From here the DC would default route it back to a redundant pair of MX units, and out to the Internet.
The AP's, now implicitly, can access the Internet and connect to the cloud.