This management is only required in acute settings or new VTE. Asymptomatic patients doesnt need this
Amboss says "Acute management of specific thrombophilias"
https://next.amboss.com/us/article/bo0H0S?q=antithrombin%20iii%20deficiency#Z806be8cb4335923325b5f66cf492b2df
UTD "Individuals with hereditary AT deficiency with a new VTE (deep vein thrombosis [DVT] or pulmonary embolism [PE]) require treatment with anticoagulation"
UTD" In patients with incidentally discovered AT deficiency (ie, without a personal or family history of thrombosis), we would use prophylactic anticoagulation only during periods of increased thrombotic risk (eg, following major surgery); we generally would not undertake prophylactic AT administration"
Source: Other - UTD: https://www.uptodate.com/contents/antithrombin-deficiency?search=antithrombin%20iii%20deficiency&source=search_result&selectedTitle=1%7E130&usage_type=default&display_rank=1#H20