Kanye West didn't make Taylor Swift famous.
A Thread:-

I am gonna tweet the incidents and informations with date. and if I make any mistake here, don't mind correcting me.;-;

Debut Era-

June 19, 2006

Taylor Swift releases her debut single "Tim McGraw". The track stayed on the Billboard Hot 100 for 20 weeks. It peaked at No. 40, and reached No. 6 on the Hot Country Songs chart.

Oct. 24, 2006

Taylor Swift releases her self-titled debut album, which debuted at No. 19 on the Billboard 200, holding a position on the Chart for 277 weeks and peaking at No. 5.
Notably, It's one of the longest charting album by a female artist on Billboard 200's history.

Feb. 19, 2007

Taylor Swift releases "Teardrops On My Guitar," the second single off her debut album. It stayed on the Billboard Hot 100 for 48 weeks, peaking at No. 13.

Sept. 9, 2007

"Our Song" the third single from her debut album, gets released. The track spent a total of 36 weeks on the Billboard Hot 100, peaking at No. 16. It also became her first No. 1 on the Hot Country Songs chart, spending six weeks atop the list.

Oct. 14, 2007

Swift releases her first EP, "Sounds Of The Season : The Taylor Swift Holiday Collection". The EP peaks at No. 20 on the Billboard 200 and at No. 1 on Top Holiday Albums.

Fearless Era-

Sept. 12, 2008

"Love Story," the lead single off of Taylor Swift's second studio album "Fearless" is released. The track spends 36 weeks on the Billboard Hot 100, peaking at No. 4, and hits No. 1 on Hot Country Songs....

...It also remarks her first Top-10 hit on Billboard Hot 100.
"Love Story" was a commercial success, selling over 18 million copies worldwide therefore establishing itself among the best-selling singles of all time. It is also one of the most downloaded country song.

Nov. 10, 2008

Swift’s single “Love Story” is named song of the year at BMI’s 57th Country Awards, making it Swift’s second consecutive win in the category following her 2008 win for “Teardrops on My Guitar.”

"Love Story" on charts and it's certifications.

Nov. 11, 2008

Taylor Swift releases her second studio album "Fearless". The album held the No. 1 position on the Billboard 200 for a total of 11 non-consecutive weeks, becoming the then longest chart-topper by a female country artist....

..."Fearless" was a worldwide commercial success. It is certified Diamond in USA. It has sold over 12 million certified units worldwide.

Certifications and Charts -

Feb. 8, 2009

The singer performs her song "Fifteen" with Miley Cyrus at the 51st Grammy Awards. Swift goes on to win a total of seven Grammy Awards between 2009 and 2012.
Notably she is the second-youngest to win Album Of The Year at the Grammys. She has won AOTY twice there.

Jun 17, 2009

Taylor Swift releases the Music Videos for "Love Story", "You Belong With Me" and her other songs on YouTube. "Love Story" and "You Belong With Me" have surpassed 509 million and 1 billion views respectively on that platform....

..."You Belong With Me" Music Video is also the most-viewed country music video on YouTube.

Aug. 22, 2009

Taylor Swift's single "You Belong With Me" becomes her fourth No. 1 on the Hot Country Songs chart and her highest-charting hit, at the time, on the Billboard Hot 100, reaching No. 2. It was also a commercial success globally.

Charts and Certifications-

Sept. 13, 2009

Taylor Swift receives the award for best female video at the 2009 MTV Video Music Awards. During her acceptance speech, Kanye West infamously takes the stage to interrupt her saying...

..."Yo, Taylor, I'm really happy for you, I'ma let you finish, but Beyoncé had one of the best videos of all time!"
and this incident started all the drama between Kanye and Taylor.

Taylor Swift sold 7 million of "Fearless" before Sept. 13, 2009. She won a VMA award over Beyoncé and Pink despite being a country Artist. Notably, It was given on Public Vote. Love Story and You Belong With Me was already successful globally....

... She was already topping the charts despite being a country artist. So she was already famous and successful. The only person that made her famous was Taylor Swift herself.

Even if we forget these for some time, Taylor Swift sold more than 1 million copies of her 4 albums consecutively, something only The Beatles have done. She earned a #1 hit on Billboard Hot 100 with WANEGBT. Fearless is literally...

...the most awarded country album of all time. 1989 is the most awarded pop album of all time. 1989 is the second pop album to have five singles chart inside the top-10.

She was already successful before that incident. She is still successful. and Kanye West does not have any credit for her success. Kanye West never made Taylor Swift famous. Taylor Swift is famous for her creation, for her music. She herself made her famous!

End Of Thread
Source- Wikipedia, Billboard, RIAA and ARIA