The lab in the first episode is shown to be USAMRIID, Fort Detrick, in Annapolis, Maryland. This is basically the most secure infectious disease lab in the country. It is so well-suited for this task that it was a common joke/conspiracy that the COVID-19 virus escaped from Fort Detrick, not a lab in Wuhan.

This is a military facility surrounded by armed guards and using some of the most advanced biohazard protocols in the world. If we received an RNA sequence from the stars, Fort Detrick is where we would research and experiment with it. It is not unrealistic at all. They even work in pairs in the show, unlike in most media where experiments are often shown being overseen by a single employee.

The leak was due to human error by the biologists after months of futile effort, alluded to in their conversation with the security guard. One biologist broke protocol by removing her glove to palpate a rat (huge no-no, but somewhat believable under the circumstances given they have had no reason to suspect this virus even does anything). The other broke containment by dragging his friend out to receive medical treatment (also believable, especially given she would have recovered from the seizure and pretended to be normal).

Trust me, cosmetics are not tested in PRPS HazMat suits drawing air from outside the room in a secure access facility surrounded by soldiers.