Baumann represented the United States at the 2014 City of Jesolo Trophy in Italy. Baumann placed first in the team competition and second on the balance beam.
After the 2014 P&G National Championships, she was named to the United States' national team and was chosen to compete as a member of the 2014 Pan American Championships team. Baumann withdrew from the Pan American event due to a hyperextended elbow injury.
Baumann was selected to compete at the 2014 World Championships in Nanning, China, where she contributed towards the team gold medal on balance beam, her only event during the Team Final, and scored a 14.500.
On July 25, 2015. Baumann competed at the Secret U.S. Classic and finished 6th in the all-around with a score of 56.950, behind Simone Biles, Gabby Douglas, Maggie Nichols, Bailie Key, and Aly Raisman and ahead of Mykayla Skinner. She started on beam where she fell on her switch ring leap, scoring a 13.750 and finishing 10th on the event, 0.1 behind WOGA teammate Madison Kocian. She scored a 14.150 on floor, finishing 6th and a 14.500 on vault following a low, under-rotated double-twisting Yurchenko. She finished on uneven bars and scored a 14.500, finishing 6th on the event.
On August 13 & 15, Baumann competed at the 2015 P&G Championships in Indianapolis, Indiana and placed 7th in the All-Around with a 2-night total score of 115.700, tying with Mykayla Skinner.
On Night 1, Baumann started on beam where she had great difficulty that included a stuck standing Arabian and an Onodi connected to a wolf jump and scored a 15.150, the highest beam score of that night. On floor, she had a sub-par performance that included a wobble on her Memmel (double Y-turn). She scored a 13.900. She under-rotated her double-twisting Yurchenko and scored a 14.300. She ended on bars and had a good executed routine and scored a 14.500. At the end of the night she was 6th in the all-around with a score of 57.850.
On Night 2, Baumann started on floor. She stumbled out of her double turn with her leg at horizontal and missed a connection (she connects it to a single Y-turn). She scored a low 13.700 with a 5.7 start value (compared to 5.9 on Night 1). Her total of 27.600 placed her 9th on the event. On vault, she had a better landing on her double-twisting Yurchenko (with a small hop backwards) and scored a 15.050. On bars, she had trouble on her Pak Salto transition and slightly came in contact with the floor (her left foot swept the ground) and scored a 14.050, totaling to 28.550 and placing 10th on the event. She ended her night on beam where she performed well despite a wobble on her Onodi wolf jump connection. She scored a 15.050 and had a 2-night total of 30.200, placing 2nd on the event behind Biles and ahead of Kyla Ross.
Baumann was named to the Senior National Team and received an invitation to the 2015 Worlds Selection Camp in September.
Baumann went into the 2016 season as a third-year senior.
On June 4, Baumann competed at the Secret U.S. Classic in Hartford, CT. She scored a 14.750 on vault, a 13.150 on uneven bars, a 15.350 on balance beam, and a 14.750 on floor exercise. Her total score was a 58.000, putting her in third place behind Alexandra Raisman and Rachel Gowey.
On June 24 and 26, Baumann competed at the P&G Championships in St. Louis, MO. On night one, she scored a 14.700 on vault, a 12.750 on uneven bars, a 15.000 on balance beam, and a 14.500 on floor exercise, giving her a total score of 56.950. On night two, she scored a 15.000 on vault, a 14.450 on uneven bars, a 14.700 on balance beam, and a 13.850 on floor exercise giving her a total score of 58.000. Her overall score for the event was 114.950, putting her in seventh all-around.
On June 30, Baumann announced via Instagram that while in training, she hurt her elbow and would require surgery. As a result, she had to withdraw from the Olympic Trials that will take place on July 8–10 in San Jose, CA, thus ending her petition to the 2016 Rio de Janeiro Olympics. Baumann's commitment to the University of Florida's gymnastics program took a consequent effect as she announced that she would be deferring until the 2017–18 academic year to concentrate on rehab.
Baumann was born on May 17, 1998 in Dallas, Texas, to parents, Greg and Jarol Baumann. She has two sisters, Rachel and Kaylee. Rachel is an elite gymnast and trains alongside Alyssa at WOGA.
In 2015, she was diagnosed with coeliac disease. Baumann is currently in twelfth grade and attends Spring Creek Academy. Following high school graduation, Baumann will attend the University of Florida and is signed to their gymnastics team.