He did not understand what had happened
First, Voldemort did not understand the reason for his and Harry's wands connecting until Ollivander told him under torture:
“He wanted you to tell him how to overcome the connection between our
wands,” said Harry.
Ollivander looked terrified.
“He tortured me, you must understand that! The Cruciatus Curse, I-I
had no choice but to tell him what I knew, what I guessed!”
“I understand,” said Harry. “You told him about the twin cores? You
said he just had to borrow another wizard’s wand?”
—Harry Potter and the Deathly Hallows
Dumbledore understood immediately, yes, but it has always been clear that Dumbledore understands far more of most sorts of magic than Lord Voldemort.
Voldemort did not know whether it was some power that Harry possessed (perhaps as a result of his mother's sacrifice), some connection between their wands, or something else altogether. He was not about to throw away his wand, which he had been bonding with for decades, over one guess among many.
After this, he sought to borrow Lucius's wand. It was only once this course of action still (apparently) failed to overcome the bond between him and Harry that he realized he needed a different strategy.
“We were talking about the other wand, the wand that changes hands by
murder. When You-Know-Who realized my wand had done something strange,
he came back and asked about that other wand, didn’t he?”
“How do you know this?”
Harry did not answer.
“Yes, he asked,” whispered Ollivander. “He wanted to know everything I
could tell him about the wand variously known as the Deathstick, the
Wand of Destiny, or the Elder Wand."
—Harry Potter and the Deathly Hallows
Why would he not have sought the Elder Wand earlier, even before he believed he needed it to kill Harry?
- Priorities. Voldemort had many other things he needed to do, and getting the Elder Wand may not have been high on his list.
Knowledge. Voldemort did not know where to start looking for the Elder Wand until Ollivander told him.
“Mr. Ollivander,” said Harry, “you told You-Know-Who that Gregorovitch
had the Elder Wand, didn’t you?”
—Harry Potter and the Deathly Hallows
Arrogance. Voldemort has always been surpassingly confident in his own power, believing that he needs little more than tools with which to channel it. He sought the Elder Wand only out of necessity:
"The Dark Lord,” said Ollivander in hushed and frightened tones, “had
always been happy with the wand I made him—yew and phoenix feather,
thirteen-and-a-half inches—until he discovered the connection of the
twin cores. Now he seeks another, more powerful wand, as the only way
to conquer yours.”
—Harry Potter and the Deathly Hallows
As Dumbledore explained, Voldemort was contemptuous of having to rely on anything external1 to himself. He would not have liked the idea that a good portion of his achievements could be attributed to anything besides his own magical skill:
"Voldemort likes to operate alone, remember. I believe that he would
have found the thought of being dependent, even on the Elixir,
intolerable. Of course he was prepared to drink it if it would take
him out of the horrible part-life to which he was condemned after
attacking you, but only to regain a body. Thereafter, I am convinced,
he intended to continue to rely on his Horcruxes."
—Harry Potter and the Half-Blood Prince
Of course, eventually he got over this, once he decided that the Elder Wand would make him invincible.
1: Since the Horcruxes were simply pieces of his own soul, he probably did not think of them this way.