Estimates are a shape, not a number
Someone asks how long a piece of work will take. The honest answer is almost never a number, and the useful answer is almost never a single date.
A single date communicates false precision, and it destroys the information that mattered: how confident you are, and what would change your mind.
Name the unknown
Most estimates are dominated by one or two unknowns. Whether the old API supports batch reads. Whether the data is as clean as the schema claims. Whether the third party's sandbox behaves like production.
Saying "two weeks if the API supports batch reads, five if it does not, and I can find out by Thursday" is more useful than "about three weeks" — because it hands over the actual risk and gives a date for resolving it.
Time-box the discovery
If the unknown is large enough to swing the estimate by more than half, it is worth a spike. A day of investigation that turns a five-week range into a one-week range is the highest-return work available.
The failure mode is spiking forever. Time-box it, and commit to giving the estimate at the end whether or not the question resolved cleanly.