Starship development and progress [previous title: Will Musk's starship reach orbit this year?]

[LSLGuy]

Here’s a current space elevator thread with an interesting twist:

Which planet could we build a space elevator with current technology?

Say, a civilization is thriving on an Earth-like planet. Let’s assume they have exactly the same technology as we have right now or perhaps just the next 10 years, the planet has the same elemental composition (thus same density), with the only exception being size. Which radius and mass (high) thresholds would it need to have, to enable its people the space elevator? At that size, what changes would you predict on things (climate, population, etc)?