Seeking advice: Best way to approach cloud and technology job applications

I am actively looking for opportunities in Cloud, Infrastructure, DevOps, Technology Strategy, and IT leadership roles.

I have identified relevant openings at companies such as Agivant, Quanteon Solutions, Woodside Energy, Sandisk, Reflections Info Systems, SkillsCapital, and others. I also have a few publicly listed recruitment contact emails.

I would appreciate advice on:

How to write a short, effective email to recruiters or hiring teams

Whether it is better to apply first and then contact the recruiter

How to tailor my resume for Cloud Architect, Cloud Engineer, Infrastructure Architect, and Technology Leadership roles

How to follow up professionally if there is no response

Any templates, suggestions, or experiences from people who have successfully connected with hiring teams would be very helpful.