I have a similar problem, but a bit different hardware.
Router: Cisco RV320
Switches: Cisco SG300-10
Cable modem (also a Cisco) in bridged mode, connected to RV320 WAN1. Nothing connected to WAN2.
Router RV320 WAN1 gets an IP from the provider. Internal network IP on the router is static. DHCP is provided by a Linux server on the internal network.
2 SG300-10 Cisco switches provides network behind the router.
If i start a machine, at first it will connect to the network, and obtain IP address on the local network from the DHCP server, and all local resources function as they should. The routers IP and the internet through the router is not available. After some time, the router will become accessible, and the internet will work as expected.
This usually also happens when I come home from other locations, where I've used that locations network. When my tablet or laptop tries to establish connections again. It will be locked out for some time, before suddenly being able to access the internet again. Usually 15-45 minutes. internet comes somewhat later. When using laptops, it doesn't matter if I use a cabled network or WiFi, but sometimes one will work, the other not (sometimes wifi, sometimes cabled).
To me, it looks like some kind of table that needs to time out, before the same interface can be used again, after being off-network.