Baszucki was born on January 20, 1963 in Canada. He attended Eden Prairie High School in Eden Prairie, MN, where he was the captain of his high school TV quiz team. He later went on to host his own talk radio show for KSCO Radio Santa Cruz from February to July 2003. Baszucki studied engineering and computer science at Stanford University. He graduated in 1985 as a General Motors Scholar in electrical engineering.

In the late 1980s, Baszucki, together with his brother Greg Baszucki, developed a simulation called “Interactive Physics”, which was designed as an educational supplement that would allow the creation of 2D physics experiments. In 1989, Baszucki, together with his brother, founded the company Knowledge Revolution, which was based around the distribution of Interactive Physics. Originally released for Macintosh computers, Interactive Physics went on to win multiple awards.

In December 1998, Knowledge Revolution was acquired by MSC Software, a simulation software company based in Newport Beach, California, for $20 million. Baszucki was named vice president and general manager of MSC Software from 2000 – 2002, but he left to establish Baszucki & Associates, an angel investment firm. Baszucki led Baszucki and Associates from 2003 to 2004. While an investor, he provided seed funding to Friendster, a social networking service.

In 2004, Baszucki, along with Erik Cassel – who worked as Baszucki’s VP of Engineering for Interactive Physics – began working on an early prototype of Roblox under the working title DynaBlocks. It was later renamed Roblox, a portmanteau of “robots” and “blocks” in 2005. The website officially launched in 2006. In a June 2016 interview with Forbes, Baszucki stated that the idea for Roblox was inspired by the success of his Interactive Physics and Working Model software applications, especially among young students.

Baszucki spoke at the 2018 Disrupt – San Francisco conference. In 2020, Baszucki funded a study on the effect of Hydroxychloroquine on COVID-19, which showed no evidence of it preventing or treating the virus.

Baszucki lives in the San Francisco Bay Area with his wife, Jan Ellison, and their four children. In a 2020 blog post after the Killing of George Floyd, Baszucki expressed his support for the Black Lives Matter movement, expressing dismay at the large amounts of racial inequality in the United States.