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In matlab, I have shown the signal passed through the FIR filter in the time domain. Then the beginning of the signal is like the transient response. Is the result appropriate?

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Probably. Except for 1-tap filters, if your signal is of finite support, FIR filtering needs to assumes values outside the support (before and after the values you were given)), and those values are often considered to be $0$. Hence, the extended sequence $(\ldots,0,0,x[0],x[1],x[2]\ldots)$ may produce some artifacts or transients in the output around time $[0]$, depending on the continuity and smoothness of $x$ close to $k=0$.

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