That is a popular historical what-if question, and the general answer is: possibly.
When Hitler began his anti-semitic quest (before the actual Holocaust), thousands upon thousands of Jewish people attempted to escape German-occupied lands. At first his goal was only to kick them out of his country. By 1938 about one in four Jews in Germany -- approximately 150,000 -- had left on their own account. But with the annexation of Austria, another 185,000 Jews became unwanted.
Jewish refugees on the road
But where would they go? Most wanted to go the US or Palestine, but the truth is Jews were unwanted really anywhere -- especially in the US and Palestine. The US was in the midst of the Great Depression and Palestine was under mostly Arab hand. Yet the sheer volume of the thousands of refugees roaming aimlessly throughout Europe called for action by all of the world's countries.
(Disclaimer: any similarities to current events is pure historic irony.)
Hence US president Roosevelt convened a global conference to address the Jewish problem. Around 30 countries met in Évian-les-Bains, France. This event became known as the Évian Conference. The days-long conference led nowhere.
While all delegates expressed their sympathies, few countries were actually willing to take in any Jews for various reasons, and most straight-up refused. It was mostly due to their own economical and political situations, but some also due to anti-Semitic sentiments. While some countries already had a yearly quota of refugees that they were taking in -- Jewish or otherwise -- not even the US or the UK were willing to raise said quota. The Dominican Republic became known as the country that offered to take in the most -- 100,000.
Germany -- not invited to the conference of course -- closely monitored the situation and in part took advantage of the negative developments of it. The German government observed with obvious amusement how "astounding" it was that foreign countries criticized Germany for their treatment of the Jews, yet none of them wanted to open the doors to them. Hitler himself stated that he was quite willing to not just let all of the Jews go in peace, but would even help them get to their destinations:
"I can only hope and expect that the other world, which has such deep sympathy for these criminals [Jews], will at least be generous enough to convert this sympathy into practical aid. We, on our part, are ready to put all these criminals at the disposal of these countries, for all I care, even on luxury ships."
In the end, the conference was a failure. All it accomplished was to signal to Hitler that nobody was truly willing to interfere with him. Hitler saw no other alternative but to continue his quest, ultimately culminating a few years later in what he called his Final Solution: the systematic extermination of the Jewish population in Europe -- the Holocaust as we call it today.
The question now is that if other countries had accepted the Jewish refugees, would that have prevented Hitler from attempting to exterminate them? Historians seem to agree that theoretically it could have. Walter Mondale summed it up by saying:
"If each nation at Evian had agreed on that day to take in 17,000 Jews at once, every Jew in the Reich could have been saved."
Practically however it may have been different. The whole world was at a critical geopolitical and economical brink, and taking in so many refugees was simply an impossibility for most. It was this instability that eventually led to the Second World War, as Germany was thus able to race across the globe unchecked. It was with the launch of the war that the economies saw a return to normality.
After the war, things were different. The US was more able and willing to take in whoever was left of the refugees, as were other countries, including Palestine.
Albeit that is a different story.
The famous SS Exodus on its way to Palestine