I'm an Architect. Also with a long technical background. Similar size organisations. It's not normal to have admin access. Largely because that level of detail can overwhelm you. It's also easy to get dragged back into your old job if you can be dragged back. In one org I worked in where the Architects did have access (before I was one...) one of our vendors develops the habit of finger pointing when mysterious issues occurred that looked like unauthorised change. We stopped that with some config monitoring software that notified us of any settings change - but I mention it to show what can happen.
One of the hard concepts to grasp is what is Architecturally significant. Mostly that's big block level stuff, but sometimes certain details can be significant too. Working out which without looking at every detail is where your experience comes in.
Most of the time the team members doing the design and implementation work can show you the detail when you need to see it - and by asking them you can discuss what you're looking for and why. This builds up trust that your solutions aren't just ivory tower creations from some distant figure but things they're connected with.
If you must have some ability to see every little detail you could always try asking for read-only access. It might be a reasonable compromise.
This has been a bit of a rambling post, but I hope it has something useful....