Accurate measurements of sea ice thickness are critical to better understand climate change, to provide situational awareness in ice-covered waters, and to reduce risks for communities that rely on sea ice. Nonetheless, remotely measuring the thickness of sea ice is difficult. The only regularly employed technique that accurately measures the full ice thickness involves drilling a hole through the ice. Other presently used methods are either embedded in or through the ice (e.g., ice mass balance buoys) or calculate thickness from indirect measurements (e.g., ice freeboard from altimetry; ice draft using sonars; total snow and ice thickness using electromagnetic techniques). Acoustic techniques, however, may provide an alternative approach to measure the total ice thickness. Here laboratory-grown sea ice thicknesses, estimated by inverting the time delay between echoes from the water-ice and ice-air interfaces, are compared to those measured using ice cores. A time-domain model capturing the dominant scattering mechanisms is developed to explore the viability of broadband acoustic techniques for measuring sea ice thickness, to compare with experimental measurements, and to investigate optimal frequencies for in situ applications. This approach decouples ice thickness estimates from water column properties and does not preclude ice draft measurements using the same data.