The Verdict: Clear Path
With a Czech job offer you can apply for a work permit now: a blue card if the role needs higher education and pays enough, an employee card otherwise. Ask your employer about the government fast-track programmes before you file.
The blue card needs a salary of at least 1.5 times the average gross annual wage that the Ministry of Labour and Social Affairs announces each 1 May, so check the figure in force rather than one quoted second-hand. The employee card covers any skill level at no less than the minimum wage, tied to a vacancy your employer registers.
The Key and Research Staff and Highly Qualified Employee programmes, run by the Ministry of Industry and Trade, do not change the test but guarantee consular capacity and get round the quotas some missions apply. The employer applies to join them, not you.
Either permit leads to permanent residence after five years and citizenship five years later. If your standing is exceptional, also ask the embassy about permanent residence in the interest of the Czech Republic: it has no published criteria, so no promises, but it would skip five years.