Hi @theresa4 
As @Michaela has mentioned, it is truly one of the many questions debated among the Christian sphere. Please continue searching God’s Word diligently and prayerfully, and He will surely share His mind through the Holy Spirit’s guidance and conviction. But allow me to share some thought.
Regarding God drawing persons to Him,
The Bible is clear: (1) God wants ALL to be saved (1Tim.2:3,4 KJV) and, (2) He does NOT desire ANYONE to perish but would have people repent of their sins (2Pet.3:9 KJV). If this is true, then EVERY human who had the opportunity to consciously decide for him/herself may be said to have been given the chance to come—be drawn—to God. Yet only those who will make that decision to approach Him will experience that grace. And Jesus promises NEVER to reject anyone who comes to Him (Jn.6:37 KJV).
This is where faith comes into play. Will Man take God at His Word and approach His throne of grace? Or, will they just stand from afar fearing His justice might consume them?
(This reminds me of Queen Esther who experienced the gracious approval of King Ahasuerus [or Xerxes I] despite the king’s decree against unauthorized, or un-called for, approaches to his throne room [Book of Esther]. But I digress.)
Regarding the chance to be saved,
God’s revelation is NOT limited to the Bible. People will NOT be excusable of NOT hearing the gospel (Rom.1:20 KJV) because the whole creation testifies of His existence, and His testimony transcends the language barrier (Psa.19:1-4b KJV) more powerfully than any polyglot missionary ever could.
A humble heart will cause Man to seek God, a Higher Power though he might NOT know Him by name as Yahweh or Jesus. They will recognize that there is an ultimate Creator to whom they are accountable. A proud heart, however, will fashion its own “cuddly god” who will fit personal desires and whims, and become an idolater, or make a god of him/herself.
Answering the question, “Who gets drawn to Jesus?”
All who are born into this world is drawn by God to His Son. If they would respond in faith, then they will be resurrected at His Return.