In many countries you can buy Travel SIM Cards these days - look for a local provider in the country that you live in and check that they cover the country that you are travelling to.

I'm in Australia and this is just one of many providers - https://aussiesim.com.au

The chief marketing tactic of the telecommunications industry is confusion - Theresa Gattung, former CEO of Telecom NZ.

Local sim cards are another option but you're right - only people that know you're new number can you reach you.

Hope this helps!