Hi, marcofabri,
1-Before the Covid-19 pandemic, data from 122 countries indicated that on average, 31.1% of adults are physically inactive and over 80% of adolescents perform less than 60 min of daily physical activities.
You cannot omit "that" there because you have a sentence adverbial, which is "on average." With a slight change whereby the content clause follows the reporting verb "indicated" immediately, without the interference of an insert, you could omit "that":
1.a. Before the Covid-19 pandemic, data from 122 countries indicated an average 31.1% of adults are physically inactive and over 80% of adolescents perform less than 60 minutes of daily physical activities.
2- Time-efficient exercise programs that counteract physical inactivity, especially after the Covid-19 pandemic, are a recent major topic of investigation.
You need "that" above because it functions as the subject within the relative clause.