Look at alertmanager logs: journalctl -eu alertmanager (if you are running alertmanager under systemd)
Look at the network traffic: tcpdump -i <interface> -nn -s0 -vA tcp port 587
Could it be that your target host doesn't accept TLS?
Could it be that your target host has an invalid TLS certificate, or a cert which doesn't match the hostname in "########:587"? If you want to keep TLS but disable cert verification, then unfortunately there's no global smtp_tls_config; as far as I can see you have to set tls_config under the email_configs section of every individual receiver.
See: