Troubleshooting Wireguard on Ubuntu 20 on AWS (the very simple tutorial setup is not working) - wireguard

Question

I spawned two AWS EC2 machines, installed Wireguard on both.
The first machine is supposed to work as a Wireguard Server. I have opened port 51820 on the AWS firewall for incoming UDP and TCP traffic on that machine.
I added net.ipv4.ip_forward=1 to /etc/sysctl.conf on the Server machine and reloaded with sudo sysctl -p
Server's /etc/wireguard/wg0.conf:
[Interface]
Address = 10.8.0.1/24
SaveConfig = true
PostUp = ufw route allow in on wg0 out on eth0
PostUp = iptables -t nat -I POSTROUTING -o eth0 -j MASQUERADE
PreDown = ufw route delete allow in on wg0 out on eth0
PreDown = iptables -t nat -D POSTROUTING -o eth0 -j MASQUERADE
ListenPort = 51820
PrivateKey = *****************************************
[Peer]
PublicKey = aJtTwEv6LzdJx/ZEdQMSuOrslHY/AIv+e3EzI/bsMAY=
AllowedIPs = 10.8.0.2/32
[Peer]
PublicKey = eJJDZcHtVA0G5bJqXD/lj75Cbuu6Kcu4APrkZBwEAzs=
AllowedIPs = 10.8.0.3/32
[Peer]
PublicKey = MOgxJQTdIccWKwzAyS4Qt1CKZaDhP7Q8zHrRHDiRIwA=
AllowedIPs = 10.8.0.4/32
As you can see I have added 3 peers with different public keys. I followed the tutorial and ran the server via systemctl. Everything is up and running nicely.
Now the peer machine. Here, my /etc/wireguard/wg0.conf is the following:
[Interface]
PrivateKey = *********************************
Address = 10.8.0.4/24
[Peer]
PublicKey = MOgxJQTdIccWKwzAyS4Qt1CKZaDhP7Q8zHrRHDiRIwA=
AllowedIPs = 10.8.0.0/24
Endpoint = 34.235.224.92:51820
Address and public key match the values defined in the Server config. The Endpoint is the public IP of the first EC2 machine (I have used AWS Elastic IP)
I then ran sudo wg-quick up wg0 on the peer
The output is:
[#] ip link add wg0 type wireguard
[#] wg setconf wg0 /dev/fd/63
[#] ip -4 address add 10.8.0.4/24 dev wg0
[#] ip link set mtu 8921 up dev wg0
Then I run sudo wg on the peer machine, and the output is:
interface: wg0
public key: MOgxJQTdIccWKwzAyS4Qt1CKZaDhP7Q8zHrRHDiRIwA=
private key: (hidden)
listening port: 46598
On the server machine sudo wg is not showing the 10.8.0.4 peer made any handshakes:
interface: wg0
public key: uO5puRXj/XvgCH0SGoAm+8CsUmCPbmdbW3nvpTnepgY=
private key: (hidden)
listening port: 51820
peer: aJtTwEv6LzdJx/ZEdQMSuOrslHY/AIv+e3EzI/bsMAY=
allowed ips: 10.8.0.2/32
peer: eJJDZcHtVA0G5bJqXD/lj75Cbuu6Kcu4APrkZBwEAzs=
allowed ips: 10.8.0.3/32
peer: MOgxJQTdIccWKwzAyS4Qt1CKZaDhP7Q8zHrRHDiRIwA=
allowed ips: 10.8.0.4/32
There aren't any logs. I don't know where to look to fix the issue.