Government has always some degree of control over inflation in a country. For example, consider simple New Keynesian model of money market equilibrium given by:
$$M/P = L(Y,i)$$
Where $M$ is money supply, $P$ price level (positive change of which is inflation $\pi$) $L$ demand for loanable funds, $Y$ real output and $i$ interest rate.
Solving for $P$ we get:
$$P= \frac{M}{L(Y,i)}$$
Even if there is an exogenous inflation shock (e.g. supply chain issue causing drop in $Y$) government doesn't have to just passively stand and let the shock cause inflation. Government has option of increasing interest rate (interest rates are controlled by central banks which are government institutions), or government could restrict money supply $M$ again something that central bank could do (this could also be restricted by government borrowing less since the way how US central bank is set up institutionally it can create new $M$ by purchasing government debt so restricting gov borrowing would also restrict $M$ growth).
Inflation doesn't have much to do with trade per se (if one country has high inflation rate that will change the exchange rage and won't necessarily cause inflation in second country, there could be some inflation slipovers sometimes from country to country via trade but they are generally not major determining factor of inflation). You see inflation in many countries around the world because many countries are following the same fiscal and monetary policies. For example, almost every country in the world responded by strong fiscal stimulus to the covid19 crisis, and almost every country funded this fiscal stimulus by large increases in $M$ (see IMF review of government responses around the world). Also since 2008 many countries slashed $i$ to (or close to) zero. If all countries pursue similar policies then you will get similar results.
However, it is really silly to try to blame single politician or technocrat for that. Its not like Jerome Powell just sets monetary policy, and Joe Biden fiscal policy at a whim. In Fed monetary decisions are taken by the Fed’s monetary policymaking body, the Federal Open Market Committee (FOMC). When it comes to spending decisions of US (and how their are financed) that is ultimately decided by US congress. Trying to blame single or few people for current US or EU inflation would be equally foolish as trying to blame single or few banks for 2008 financial meltdown.
