In Chile's capital city, Grau attended basic and secondary education at the Raimapu School in La Florida.

He completed his BA at the Universidad de Chile Faculty of Economics and Business (FEN), in which he served as president of the Student Federation (FECh) from 2005 to 2006.

In that way, Grau was part of the presidential campaigns of Beatriz Sánchez (2017) and Boric, who won the 2021 elections against José Antonio Kast.

[6] In August 2022, already as minister, He was widely questioned for saying, in a context of high inflation, "Inflation brings costs and benefits to SMEs, unlike individuals," sayings that provoked anger in unions of small and medium-sized companies, as well as parliamentarians demanding their undergraduate and graduate degrees.

[11] In face of mounting criticism in October 2022 Grau deleted the tweets and said that "that these were said in specific context" adding that "I do not share [these comments] now".