Lightroom defines a "containing box" for export, where the image is maximised to "at most" dimensions in either direction. You cannot set an "at least" figure.
If you wanted to confirm that the images you are exporting, only include ones that NATIVELY have at least 2000px within their short edges as cropped - before any output resizing happens - you could include that check, as one of the rules for a Smart Collection: "Short edge" / greater than / "2000"
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