No, a G Suite admin cannot access your Google Drive files without your permission. Your files are securely stored and only you have access to your files unless you allow someone else access. G Suite admins only have the ability to manage user accounts and settings.
You can also customize G Suite settings to determine who can access your content and view your data. Here are some steps to follow to protect your files:
Manage sharing settings: It's easy to customize file-sharing settings with G Suite. You can easily restrict who can access your files from anywhere on the internet.
Set ownership: When sharing a file, you can designate whether people have view-only access or can edit the files.
Monitor activity: G Suite provides insights into user activity so you can monitor the sharing of your data.
Use access controls: You can use access controls to restrict user access to specific files or folders and also set expiration dates for grants of access.
For more information about how to keep your data secure, please see this help article from Google. https://support.google.com/a/answer/6148841