There's definitely a period in a startup where founders or management end up handling a lot of minor tasks like this, before hiring admin support staff. I personally would rather pay for services (garbage collection, catering, copier repair, etc.) vs. hiring an admin person to do this, because managing yet another employee (and one from a different background than engineers) adds stress to my life.
If I had a great candidate for admin/manager, maybe I'd consider it, but I could easily see getting to 20-30 employees before doing so.
That makes sense, and follows with my general experience: once your team reaches >= 8 people, there will always be one of them having a Major Life Issue (cancer, drugs, burnout, divorce, etc.) that will consume incredible amounts of your time too.
If you're stuck hiring them on your own (i.e. not part of a big company that has its own infra for hiring and training staff employees), several of my buddies who have started smaller companies swear by temp agencies. Quickly scan a few resumes, do a couple of chats, and then bring them onboard for a few weeks or a month in a try-before-you-buy role.
Also, if your admin does not _remove_ stress from your life, they're doing it wrong. Having had both decent and great admins, I can say that a great admin is an incredible enabler. Need your schedule to always have a three hour block of uninterrupted work time? Hate responding to urgent-but-unimportant crises that people always email you about? A professional, organized, and utterly ruthless admin is net positive w.r.t. your time and stress far more than they will ever be paid.
If I had a great candidate for admin/manager, maybe I'd consider it, but I could easily see getting to 20-30 employees before doing so.