Can thyroid goiter be prevented?

Some are caused. By iodine deficiency, which is a reason for iodinized table salt...Those lacking seafood in the midwest and near west used to be so afflicted. Taking exogenous thyroid hormone (thyrolar, synthroid) may turn off TSH stimulation and reduce/diminish growth, but that is treatment rather than prevention.
Prevention . Not really unless it's due to iodine deficiency. Most goiter is inflammatory due to autoimmune antibody reaction. No way to prevent this.