It is not possible to search for contacts who did not open a campaign(s) within a specific time frame. However, you can search for contacts who have not opened a specific campaign(s) by creating an advanced search or by viewing the non-opens in your campaign reports.
You can also implement the Engagement Tagging automations to begin tracking which contacts are or are not engaged with your communications. These two automations work together to apply and remove engagement tags to your contacts, based on their interactions with your communications.
These two recipes are located in the "Create a New Automation" modal that appears when you click "New Automation."
Once these automations are implemented in your account, they will only consider engagement moving forward. They cannot determine engagement for previously sent campaigns. We recommend documenting the date that these automations are activated in your account; this will give you a frame of reference as to when the non-engagement tags are applied to your contacts.