This is an excellent question, it shows that you are thinking analytically and very deeply about these issues.
When a router sends an OSPF hello packet, it sends it to the 188.8.131.52 multicast address. When R2 receives this packet, one of the pieces of information it receives in the OSPF header is the IP address of the router that sent it.
Now the next step to establishing a neighbour adjacency is for R2 to respond with a unicast packet sending its router ID and its neighbour list. However, in order to do this, it must encapsulate the response, which is an IP packet, into a frame. In order to do that, it must learn the destination MAC address, something it does not yet have in its ARP table since the initial communication was a multicast packet. So it initiates an ARP request for the IP address of R1 and receives the MAC address. It can then further encapsulate the frame and send it on its way.
I hope this has been helpful!