It's the 'foot in the door' - once your on this side of it, it's up to what you do with it.. Once your in, script your job to make life easier for you, while also doing everything 100% with out failure (assuming your scripts aren't full of bugs) - you will get promoted into another position - or simply ensure that you keep your job. If you don't get promoted, jump jobs - its basically ALL experience that gets you the higher end positions, nothing else, certs help with the bigger companies, smaller ones (where I prefer) want experience more than anything. Jumping jobs, ensures you get the varied experience. Multiple steady jobs as a sys admin, could land you the Sr Sys Admin in a smaller company.
Also, don't stop with just installing systems on new hardware, thats easy - try to get your hands on the 'old' stuff that barely works, and I'm talking Pentiums - nothing in the last decade. back when I was a teenager, my mom was given around a dozen plus systems for a project she was working on, she tasked me with seeing what worked and what could be done with them. I was able to get around 7 systems fully working, only some had no drives. Between them all, I got into networking (obviously), diskless nodes, DNS, various services, the kernel/modules/configurations, etc.., etc.. Because the amount of resources I had to work with was very limited, I had to really do my homework to get everything going AND usable. A few years later, my first 'good' job I scored because I knew what some strange boot codes from LILO were when simply no one else did, and I could get the critical systems going again (I was contract initially) - I only knew that info from the countless issues I ran into on that old hardware, and getting it all working.
When it comes to your employer verifying that you can walk the walk, and not just talk the talk - it's done one of two ways, and sometimes both - they will either verify from word of mouth (previous employer/references) or during your 30 day/3month 'probation' period.