Fast letdown makes baby cough

Hey BF mamas - anyone else have a fast/strong letdown that makes baby choke and cough? If so, what do you do to deal with it? My 3.5 week old has been struggling with my letdown since being a week old. It happens almost every time - she starts to cough and cry when letdown happens, or she ends up gulping a bunch of air and needs to stop to have a massive burp before wanting to nurse again. I always feel so bad 😞 Ive tried reclining back, but she doesn’t seem to like to nurse face down. I asked my lactation consultant about it and she didn’t seem concerned and told me when babies cough/choke on breast milk that it actually puts antibodies in their system (?)🤷🏻‍♀️ Which is great and all, but just wondering if/when we will be able to have a nice peaceful nursing session without coughing. Baby does have a “very mild” tongue tie, but the doctor and lactation consultant said it didn’t look like it’s impeding her tongue.