Yes, WooCommerce can help with this. You can use WooCommerce Analytics → Revenue/Orders and filter or export your orders by billing/shipping country, then total the qualifying sales for EU countries. For a more convenient country-by-country report, there are also WooCommerce reporting extensions that provide sales by country.
One thing to double-check, though: the €10,000 EU threshold depends on the type and origin of your sales. It isn't simply a €10,000 limit for "imports into the EU." So I'd verify your specific situation before using that figure for VAT purposes.
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