You have to share more details on the design to tell you more
1> IP addressing scheme/ VLAN details.
2> Are the same VLAN's are already available in Site2 , as from the diagram it seems you can have same vlans extended being connected in same cores.
3> You can plan to migrate based on vlans/subnets, By configuring a new gateway/interface IP on Fortigate and then changing the routes.
ROSA Technocrat - Also on youtube