I’m not certain what precisely mental health first aid training entails and thus it’s difficult to answer your question. Not knowing your brother and his personality also adds to my difficulty in answering your question.
In general, there’s no harm in asking him. Let him decide what he wants to do. He may say no and then you’ll have your answer.
If he says no, don’t pressure him. Eventually, he may take your advice but understand that your power is limited. Understandably, you’re trying to help but you can’t force people to do things they don’t want to do.
He may be unwilling to participate in psychotherapy at this time but at least he’s taking medication. That shows that he’s willing to at least partially engage in treatment, which could provide symptom relief. He may be more open to additional help in the future. I hope so because depression is well treated by psychotherapy.
Finally, try contacting your local National Alliance on Mental Illness (NAMI). NAMI is an advocacy organization that assists individuals who have a loved one with mental illness. They provide support and guidance to family members in situations like yours. Good luck and please take care.
Dr. Kristina Randle