Could a larger shore battery have taken San Lázaro?

Could the British have taken San Lázaro with a stronger shore artillery effort?

Possibly: 30 to 40 properly emplaced heavy guns might have made a practicable breach, but the expedition lacked the engineering capacity to create that battery.

About twenty landed 24-pounders successfully breached the smaller outer fort. A battery of perhaps 30 to 40 guns might therefore have broken San Lázaro's walls and opened the way to dominate Cartagena. The essential condition was a properly constructed shore position; without a breach, infantry and undersized ladders could not solve the problem.