A player may only choose a lesser bonus if they have matched enough icons for a higher bonus. Specifically:

• If a player matches 2 icons, they can choose to take the lesser bonus for matching only 1 icon.
• If a player matches 3 icons, they can choose to take any 1 of the lesser bonuses instead.
• However, if a player does not match at least 1 icon (i.e., does not meet the minimum threshold for any bonus), they do not receive a Day Bonus.

This is supported by the following rule:

"A player who has matched 2 icons can choose to take the lesser bonus for matching only 1 icon. A player who has matched 3 icons can choose to take any 1 of the lesser bonuses instead. No additional bonuses are earned for matching 4 or more icons to the Favorable Condition token for a single day."
(page 8)

Therefore, if a player cannot fulfill the requirements for any available Day Bonus (i.e., they have not matched at least 1 icon), they simply forfeit the bonus and do not receive any Day Bonus.

Source: page 8

Source: Base Rules (pp. 10, 15, 7, 8)