How can I estimate or control the soft start time for TPS73801-SEP
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The TPS73801-SEP does not have a soft start circuit.
Currently the only space grade LDO with integrated soft start is the TPS7H1101A-SP.
There is a TI application note on adding soft start to an LDO externally. This may or may not be a suitable option for your design.
See this application note.
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I wanted to add a couple more comments that may be helpful.
If the LDO is coming up with Vin Ie, EN tied to Vin, then the inrush current will be somewhat softened by the ramp rate of Vin.
If Vin is powered up, with device disabled, then EN is set to high, the inrush current will be significant. Potentially up to the internal current limit of the device until Vout is regulated.