Key Inclusion Criteria:
All Patients:
* Age ≥ 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status of ≤1.
* Adequate end organ function.
* Ability to swallow oral formulations.
* Ability to understand and willingness to sign the ICF.
Part A:
* Histologically confirmed locally advanced unresectable/metastatic HCC or histologically confirmed advanced solid tumor with documented FGF/FGFR pathway alterations
* For participants with histologically confirmed locally advanced or metastatic HCC:
* Barcelona Clinic Liver Cancer (BCLC) stage B that is not eligible for locoregional therapy, or stage C.
* Child-Pugh Score class A
* Must have previously received SOC appropriate for their tumor type. Any number of prior therapies, including FGFR inhibitors, are permitted.
* Agree to provide archival tumor tissue no older than 2 years from the time of enrollment, if available. If an archived specimen is not available, a biopsy is not required.
Part B, Cohort 1:
* Histologically confirmed locally advanced/metastatic HCC who have previously received standard of care.
* Barcelona Clinic Liver Cancer (BCLC) stage B that is not eligible for locoregional therapy, or stage C.
* Child-Pugh Score class A
* Availability of an archival formalin-fixed paraffin-embedded (FFPE) tumor tissue specimen obtained ≤2 years prior to screening for submission to sponsor-designated central laboratory for FGF19 IHC testing.
* At least 1 measurable lesion by RECIST v1.1.
Part B, Cohort 2:
* Histologically confirmed advanced solid tumor except FGFR3-altered urothelial carcinoma and primary central nervous system tumors who have previously received standard of care. Note: Participants with confirmed diagnosis of locally advanced or metastatic HCC are not eligible for Cohort 2.
* Must have an eligible activating gain-of-function alteration in the FGFR3 or FGFR4 gene, or focal amplifications of FGF19
* Archival tumor tissue biopsy specimen no older than 2 years from the time of enrollment, if available. If a tissue biopsy specimen is not available, a biopsy is not required.
* At least 1 measurable lesion by RECIST v1.1.
Key Exclusion Criteria:
All Patients:
* Have disease that is suitable for local therapy administered with curative intent.
* Have not recovered from reversible toxicity of prior anticancer therapy to \< Grade 1 or baseline (except toxicities that are not clinically significant or not expected to resolve, including but not limited to, alopecia, fatigue, skin discoloration, or Grade 1 neuropathy).
* Have received the following anticancer therapy:
1. Any immunotherapy or other antibody therapy within 28 days prior to the first dose of the study drug.
2. A TKI \< 5 days or 5X the terminal Phase elimination half-lives, whichever is longer, prior to the first dose of TYRA-430.
3. Other systemic therapy not listed above \< 14 days prior to the first dose of the study drug.
* Participant discontinued a prior anti-FGFR therapy due to significant toxicity, defined as hepatotoxicity ≥ Grade 3 or any Grade 4 toxicity according to CTCAE v5.0.
* Has a serum phosphorus level \> upper limit of normal (ULN) during screening that remains \>ULN despite medical management.
* History of or current uncontrolled cardiovascular disease.
* Active, symptomatic, or untreated brain metastases.
* Have a diagnosis of primary CNS malignancies.
* Gastrointestinal disorders that will affect oral administration or absorption of TYRA-430.
* Females who are pregnant, breastfeeding, or planning to become pregnant and males who plan to father a child while enrolled in this study.
* Any reason that, in the view of investigator, would substantially impair the ability of the participant to comply with study procedures and increase the risk to the participant.
Part B, Cohort 1:
* Known fibrolamellar HCC, sarcomatoid HCC, or mixed cholangiocarcinoma and HCC.
* Prior treatment with pan-FGFR inhibitors or FGFR4-selective inhibitors.
Part B, Cohort 2:
* Histologically confirmed locally advanced/metastatic HCC.
* Histologically confirmed urothelial cancer.
