I agree with the other answers. I have never heard or used “front this week”

'Early this week' would indicate sometime in the beginning of the the week (say Sunday - Tuesday) 'Earlier this week' would indicate ANY day prior to the current day (usually 2+ days as if it were only one day 'yesterday' would be used), but still within the same week. 'Front this week' is not used and sounds awkward.

"early this week" = sometime during the first half of the week, like maybe Sunday, Monday, or Tuesday "earlier this week" = anytime time this week before now; for example, on Saturday I might say, "I saw him earlier this week" - this might mean Thursday, even though Thursday is one of the later days of the week "front this week" isn't a phrase, but you might mean "front OF this week" - this is not a common phrase in the U.S.; I'm not sure about other English-speaking countries

Do you mean, "before this week", or "at the beginning of this week"? "Front this week" has no meaning.