What time should I drink soy milk everyday?

Why drink soy? Unless you are on certain medications (e.g. Doxycycline, thyroid supplements, etc) you probably don't need to time the soy milk intake. I would argue that you shouldn't be drinking soy milk everyday especially if you have history of thyroid disease. Soy(like other goitrogens) competes with thyroid hormone receptors in the body and may lead to low thyroid function. Why not try almond milk?
Any time... You can drink that any time of the day...There is no rule for this.....If, however, you have bad trouble with reflux etc...It may not be a good idea to have a stomach full of anything before hitting the sack... Otherwise, drink your soy to good health... Good luck.