Ps 9:16 says, " The Lord is known by the judgment which he executeth." His judgments, statutes, and precepts of the kingdom are contained in the righteous law called the New Covenant,
The Father revealed to Peter, through that covenant given and guaranteed by the blood by Christ, Acts 4:12 that "Neither is salvation in any other; for there is none other name under heaven given among men, whereby we must be saved."
The Father limits himself by his covenant, This in no way limits his sovereignty but the covenant reveals that by which he will accomplish his will for his people and the way they are to walk. As Heb 8:5 says when the Father gave commandment unto Moses, "See saith he that thou make ALL things according to the pattern shown thee in the mount." We are to build according to that covenant pattern given unto us by the Father. This is also why we are not to add to nor take away from the scriptures (covenant). When the foundation is wrong then the whole building ends up being wrong.
The Father is not a double minded man. (James 1:8) James further brings out in the 17th verse that with the Father of lights, "...with whom is no variableness nor shadow of turning." Acts 4:12 lays a foundational truth by which we know the means of salvation. Ps 11:3 says, "If the foundations be destroyed, what can the righteous do?" Therefore he DOES NOT declare the name by which man can be saved then change that foundational truth. He DOES NOT say to one group, "I will bring you in by the gospel of Christ" then to another group "I will bring you in by some back door." That line of interpretation attempts to rob Christ of his glory under a false understanding of the sovereignty of God. Christ says in Jn 14:6, "I am the way" or the pattern and therefore prevents, by self limiting salvation to himself, any other way to the Father.
I would not give you ten cents for all the claims of people being saved by bibles falling out of airplanes or tracts being found on the ground. Paul says in Romans 10:14, "How then shall they call on whom they have not believed? and how shall they believe on whom they have not heard, and HOW SHALL THEY HEAR WITHOUT A PREACHER? The Ethiopian treasurer witnesseth the same. His reply when Phillip asked him if he understood what he was reading, "How can I except some man should guide me?"
As with the Ethiopian treasurer, the Lord sent deliverers to old covenant Israel, even when they were scattered under every nation under heaven. The pattern has not changed. When the Lord is ready to deliver his people, he will provide them with a witness who will tell them of the Deliverer. This is the sovereignty of God.