Can I setup an email server to receive emails faster

I'm subscribed to a web service that sends periodic email mailouts.

My task is to get these with the lowest possible delivery latency.

What can I do to minimize latency? And what is a realistic expectation for achievable latency? Is it in the order of milliseconds or seconds?

Supposing I were to set up my own email-server near to the server of the sender... what could I do to minimize latency?

e.g. Can I infer the platform of the outgoing mail-server and if so, can I make use of that information?

you could increase the "TCP Window-Size"-Parameter (the "receive Window", "Scaling factor") of the operating system running your mail-server.

Doing that, the sender - if it accepts that which isn't unlikely today - could send larger chunks of TCP-Data without the need to get the correct reception acknowledged by the receiver.

This doesn't reduce the end-to-end Latency, of course - but it reduces the amount of times this latency is taken into account.

What can I do to minimize latency?

You can't do anything. You have no access to, nor control of, the sending system nor any of the intermediate systems that the email may flow through. Geographic proximity is unrelated to the speed of the email transmission at the application layer.

And what is a realistic expectation for achievable latency?

You should have no expectation as to achievable latency. SMTP is a "best effort" protocol and to my knowledge none of the SMTP related RFC's specify or designate anything related to ultimate deliverability or the speed thereof.

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.

Do a-mail@a-example and a-mail@z-example receive the message before z-mail@a-example and z-mail@z-example ?
Then you can game the system at the sender side because they send out their email messages by ordering the mailboxes alphabetically.

Do a-mail@a-example and z-mail@a-example receive the message before a-mail@z-example and z-mail@z-example ?
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.