We are all on a journey in our lives. Knowing and feeling God’s love is something that for some of us is immediate and real and self evident, but for others requires grace and much searching. Through following His ways, listening to His Word and reception of the Sacraments, God will form you to Him. The more you follow His ways, the easier it becomes to know Him and to comprehend the enormous depth of His love for us. He is righteous and just and His love is thus righteous and just, but He has the love of a Father for us, so much so He was willing to go as far as giving everything for us, as MarcoPolo vividly illustrated above. Through the Incarnation, He united Himself to us, so that we might enter into the life of the Holy Trinity and “become like God”.
I think,since you mention “a true connection,” that you may be trying very hard for a “feeling” because that’s usually what we mean when we talk about love, but the Love of God for His children is so much more than that - it is of course more than any of us can ever imagine or conceive of, because He is infinite. Your idea that it is “like” the love parents have for their children is completely scriptural, as is the analogy of the love between lovers (Song of Songs) or the love of a man for his wife, even if she is repeatedly unfaithful (Hosea).
God’s love is not a pampering love; it’s a perfecting love