You are correct that that all companies pay corporate taxes. We have established that.
VAT is already baked into the cost of production at every step in a VAT-based economy. If VAT were not refunded, that 19% tax cost would be included in the price, making the bulldozer more expensive abroad. Technically, VAT refunds are not an "export subsidy" in the traditional sense (where the government directly pays companies to export). BUT, the effect is the same as a subsidy and it removes tax costs from exports, giving VAT-based economies a competitive advantage. The US does not provide tax relief for its exporters and does not impose VAT on imports.
"Everyone is on a level playing field"
Wrong. The US does not refund taxes on exports, while VAT countries do
When you are ready to understand that part let me know.