If a Mirai bot sends a TCP SYN to some port … to my router’s public IP, assuming there is no port forwarding already on the router for 5555 can that TCP packet even reach devices inside the house
Provided that no port forwarding is done, no connection establishment can be done from outside. This includes SYN scanning. See also Scan a computer behind NAT.
Does this also mean people using devices behind router don’t have to worry about their devices being infected with Mirai ?
There is Mirai like you describe and there are different variants of Mirai, i.e. it evolved and also changed behavior. One of the variants directly addresses vulnerabilities in the router, i.e. does not need to rely on port scanning. See 100,000-strong botnet built on router 0-day could strike at any time.
Is there any way attacker can overcome this situation to reach the device behind the router ?
Apart from vulnerabilities in the router: Even if there is no explicit port forwarding is configured there can be port forwardings caused by UPnP. And there can be tunnels to the inside created by issues like NAT slipstream. Apart from this internal devices might be attacked using CSRF or similar, which also might be used by an attacker to add explicit port forwardings to a vulnerable router.