Override inline CSS from CSS file without !important

No.

The only way to override a CSS rule without using !important is to use a more specific selector.

No selector is more specific than the style attribute.

If we think about this differently considering that you want to override width/height then yes you can do it with min-width/min-height:

#my_component {
  min-width:200px;
  min-height:200px;
  background:red;
}

<div id="my_component" class="class_1" style="width: 40px; height: 40px;"></div>

And to be more accurate you can add the max-* version to be sure you have a fixed height/width:

#my_component {
  min-width:200px;
  min-height:200px;
  max-width:200px;
  max-height:200px;
  background:red;
}

<div id="my_component" class="class_1" style="width: 40px; height: 40px;"></div>

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