First, election of Hamas and Hamas affiliated seats is very different than support for Hamas. These were local representative elections, not a national party election like Israel. So the 58% number seems misleading. And the reason there have not been elections since 2006 has much more to do with Hamas being unwilling to have elections than you seem to think
Second, I think there is a critical difference between support for a political group and support for violence. Most Gazans did not want violence, and a majority of Palestinians, when polled, would accept peace under various terms—they no longer support a two state solution with the current borders, though they did a decade ago, especially because such a deal still leaves Israel in control of the borders. However, there are a variety of scenarios which include concessions Israel is unwilling to offer, for political and/or security reasons, that would have a solid majority of Palestinians supporting a deal.
The Hamas holds 56% of the Palestinian Legislative Council seats, elected democratically in 2006. Neither Presidency nor legislative council elections have not been held since 2006, because Hamas would win them.
What evidence do you have for a silent, peaceful majority?
First, election of Hamas and Hamas affiliated seats is very different than support for Hamas. These were local representative elections, not a national party election like Israel. So the 58% number seems misleading. And the reason there have not been elections since 2006 has much more to do with Hamas being unwilling to have elections than you seem to think
Second, I think there is a critical difference between support for a political group and support for violence. Most Gazans did not want violence, and a majority of Palestinians, when polled, would accept peace under various terms—they no longer support a two state solution with the current borders, though they did a decade ago, especially because such a deal still leaves Israel in control of the borders. However, there are a variety of scenarios which include concessions Israel is unwilling to offer, for political and/or security reasons, that would have a solid majority of Palestinians supporting a deal.