Proof of work.

Determine what being a strong family means to you. Find out what it means to your family members. Get on the same page in terms of what your family goals, values, and ideals are and work together to get there. Get on the same page in terms of where you are willing to compromise as well. You will never all agree on everything. What are you willing and unwilling to compromise on?

For instance, with my kids I am unwilling to compromise on effort, if they are going to do something I expect a full effort or don't bother but I also have to accept that sometimes they will say "I really don't want to do that" and I have to cut them some slack. Yesterday my son did not want to come with us to visit my parents. He wanted some free time for himself after catching up on a lot of school work during the week. I was disappointed because my attitude is "you don't know how long your grandparents will be around, you should spend every minute you can with them" but I also don't want to force him to go and be miserable so I let him stay home and told him "I would like you to come with me to see them next week" and he said "ok, I will".

I think a strong family means that people are count-on-able... that is, you have a network of people who you can rely on for various support. You know you can call on them to watch the kids, help with the house upkeep, etc.

I think leadership from the top - you and your spouse - showing love, understanding, discussion, etc. - that you can have a disagreement but you still love each other and work it out.

Going through hard times together, working together, reflecting, growing ...

Then there's the raising of the kids within your household - teaching kids to be respectful, feel safe, smart, thoughtful - all the things.

... there's a lot, this is just off the top of my head

I think respect and trust are huge. It helps everyone go through their tasks with positivity and purpose. If you think you are being sabotaged or it is a waste, no one will be motivated.

Like any relationship, it boils down to communication, caring and supporting each other

Willing participants.

To be practical, TRUST no doubting each other. Be transparent always be in honest direction and dont leave just because had a fight.

This paragraph is from family proclamation of my church: Husband and wife have a solemn responsibility to love and care for each other and for their children. “Children are an heritage of the Lord” (Psalm 127:3). Parents have a sacred duty to rear their children in love and righteousness, to provide for their physical and spiritual needs, and to teach them to love and serve one another, observe the commandments of God, and be law-abiding citizens wherever they live. Husbands and wives—mothers and fathers—will be held accountable before God for the discharge of these obligations.

I've found Jesus until quite recently (it has been bit under three years since my baptmism), but it has dramatically changed my life and view of family towards more positive. I know also what life is without gospel of Jesus Christ. Overall this and the family proclamation as a whole do answer this question in my opinion: https://www.churchofjesuschrist.org/study/scriptures/the-family-a-proclamation-to-the-world/the-family-a-proclamation-to-the-world?lang=eng

I expect the answer you will most gravitate to is hinted at in your choice of words. "Forge" certainly denotes something made to be strong, but it also evokes an ironically antithetical image (since to forge something is also to create a fake).

As drawn from a metallurgic context, a forge is to shape and strengthen a metal through repeated heating and beating. It is forceful, exhausting work that creates objects of immense strength and ingenuity. Some might guffaw at the idea that this same sense applies to families, but I would argue that they are taking for granted the benefits of experiencing adversity as a team as well as the benefits from strong, purposeful leadership. (Disclaimer: do not heat or beat your families.)

I think a father can bring this quality to the family by way of introducing the family to experiences that forge their bonds and other strengths. Family vacations, adventures, chores, charitable acts, moments of humility and forgiveness--all of these situations and more can test a family and have them coming out the end of it stronger. The father's role can be knowing what tests and experiences are appropriate for his family and to be their protector through it. I think it would also be his challenge to know that he is not separate from these tests.

Another verb you could have used is "grow." There are plenty of phenomena in nature that show how growth can lead to remarkable strength. An oak tree comes to mind. This might be a word better suited for a mother (though a father is not completely exempt). Growing requires patience, nourishment, and sacrifice--these are also motherly traits that might contribute to a strong family.

I have more to say on the matter, especially more specific to your questions, but I leave this reflection on the question itself for now.

A strong family is only possible when the husband and wife are intelligent people. How can fools create a strong family? Never!