It's 100% possible.
However, some peculiarities with VA hiring can impact securing a job. For example, many positions may give some preference to current employees of that facility, current employees at that VISN (region), current federal employees, etc. Plus they will also have familiarity with VA processes and culture.
However, there are also VAs that typically can't hire or retain, often in less desirable areas where they'd be thrilled to hire anybody to help with backlog.
Lastly, some VAs tend to fill a lot positions with direct hires so you may never see those positions on USAJobs. The facility where I did my postdoc did a lot of inter-facility transfers for desirable openings and then will hire on postdocs for general openings.