Inclusion Criteria:

Phase 1 Part A and Part B

1. Men and women 18 years of age or older.
2. Eastern Cooperative Oncology Group (ECOG) performance status of ≤1.
3. Histologically confirmed advanced solid tumor who have exhausted standard therapeutic options.
4. Evaluable (Part A) or measurable (Part B) disease according to RECIST v1.1.
5. Histologically confirmed advanced solid tumor with an eligible FGFR3 gene mutation or fusion (Part B).

Phase 2

1. Men and women 18 years of age or older.
2. ECOG performance status of 0-2 or Karnofsky Performance Scale (KPS) >70.
3. At least 1 measurable lesion by RECIST v1.1.
4. Histologically confirmed locally advanced/metastatic tumor in one of the following categories:

1. Urothelial carcinoma with an eligible FGFR3 gene mutation or rearrangement who have progressed on a prior FGFR inhibitor and presence of a resistance mutation or other kinase domain mutation.
2. Urothelial carcinoma with an eligible FGFR3 gene mutation or rearrangement who has not received a prior FGFR inhibitor.
3. Any solid tumor with an eligible FGFR3 gene mutation or rearrangement.

Exclusion Criteria (All Phases):

1. Has a serum phosphorus level > upper limit of normal (ULN) during screening that remains >ULN despite medical management.
2. Any ocular condition likely to increase the risk of eye toxicity.
3. History of or current uncontrolled cardiovascular disease.
4. Active, symptomatic, or untreated brain metastases.
5. Gastrointestinal disorders that will affect oral administration or absorption of TYRA-300.
6. Females who are pregnant, breastfeeding, or planning to become pregnant and males who plan to father a child while enrolled in this study.