You don't have control over what happens at the sender side in their infrastructure, but you can attempt to subscribe with several different mailboxes and domains to see if email addresses are processed alphabetically by mailbox and/or mail domain or for example in order of an ID number that reflects on their sign-up date.
a-mail@z-example receive the message before
Then you can game the system at the sender side because they send out their email messages by ordering the mailboxes alphabetically.
z-mail@a-example receive the message before
Then you can game the system at the sender side because they send out their email messages by ordering the mailboxes alphabetically by domain name.
For my own mail servers, the most delays incoming mail messages incur before they arrive in my mailbox are due to anti-spam and anti-virus measures.
It is up to you and the capabilities of your mail server is you and want to disable those for that particular sender and/or recipient.
Normally the delays start with the reverse DNS lookup of the IP-address the sender is using by the incoming mail server. - You can avoid/minimise that by hard coding the senders IP-address in for example a hosts file.
Maybe your anti-spam and anti-virus solutions feature an exemption list of trusted senders and/or recipients for which you can disable them.