By default Magento collapse all filters in layered navigation. So if you want to expand only “Category” filter please follow below steps.

First you have to override below PHTML file in your theme:

vendor/magento/module-layered-navigation/view/frontend/templates/layer/view.phtml

1	vendor/magento/module-layered-navigation/view/frontend/templates/layer/view.phtml

Like:

app/design/frontend/[VENDOR_THEME_NAME]/[THEME_NAME]/Magento_LayeredNavigation/templates/layer/view.phtml

1	app/design/frontend/[VENDOR_THEME_NAME]/[THEME_NAME]/Magento_LayeredNavigation/templates/layer/view.phtml

After overriding above PHTML file find below code and replace with new code (Around line no. 33 to 42):

<?php foreach ($block->getFilters() as $filter): ?>
    <?php if (!$wrapOptions): ?>
        <strong role="heading" aria-level="2" class="block-subtitle filter-subtitle"><?= /* @escapeNotVerified */ __('Shopping Options') ?></strong>
        <dl class="filter-options" id="narrow-by-list">
    <?php $wrapOptions = true; endif; ?>
        <?php if ($filter->getItemsCount()): ?>
            <dt role="heading" aria-level="3" class="filter-options-title"><?= $block->escapeHtml(__($filter->getName())) ?></dt>
            <dd class="filter-options-content"><?= /* @escapeNotVerified */ $block->getChildBlock('renderer')->render($filter) ?></dd>
        <?php endif; ?>
<?php endforeach; ?>

<?php foreach ($block->getFilters() as $filter): ?>

<?php if (!$wrapOptions): ?>

<?php $wrapOptions = true; endif; ?>

<?php if ($filter->getItemsCount()): ?>

<dt role="heading" aria-level="3" class="filter-options-title"><?= $block->escapeHtml(__($filter->getName())) ?></dt>

<dd class="filter-options-content"><?= /* @escapeNotVerified */ $block->getChildBlock('renderer')->render($filter) ?></dd>

<?php endif; ?>

<?php endforeach; ?>

Replace with this code:

<?php foreach ($block->getFilters() as $filter): ?>
    <?php if ($filter->getItemsCount()): ?>
        <?php if (!$wrapOptions): ?>
            <?php  
                $collapsibleRange = '';
                $cat = __('Category');
                if($filter->getName() == $cat){
            	   $collapsibleRange = $catcount; 
                }
                $catcount++;
            ?>
            <strong role="heading" aria-level="2" class="block-subtitle filter-subtitle"><?php /* @escapeNotVerified */ echo __('Shopping Options') ?></strong>            
            <dl class="filter-options" id="narrow-by-list" data-role="content" data-mage-init='{"accordion":{"openedState": "active", "collapsible": true, "active": "<?php echo $collapsibleRange ?>", "multipleCollapsible": false}}'>
            <?php $wrapOptions = true; ?>
        <?php endif; ?>
        <div data-role="collapsible" class="filter-options-item">
            <div data-role="title" class="filter-options-title"><?php /* @escapeNotVerified */ echo __($filter->getName()) ?></div>
            <div data-role="content" class="filter-options-content"><?php /* @escapeNotVerified */ echo $block->getChildBlock('renderer')->render($filter); ?></div>
        </div>
    <?php endif; ?>
<?php endforeach; ?>

<?php foreach ($block->getFilters() as $filter): ?>

<?php if ($filter->getItemsCount()): ?>

<?php if (!$wrapOptions): ?>

<?php

$collapsibleRange = '';

$cat = __('Category');

if($filter->getName() == $cat){

$collapsibleRange = $catcount;

}

$catcount++;

<dl class="filter-options" id="narrow-by-list" data-role="content" data-mage-init='{"accordion":{"openedState": "active", "collapsible": true, "active": "<?php echo $collapsibleRange ?>", "multipleCollapsible": false}}'>

<?php $wrapOptions = true; ?>

<?php endif; ?>

<div data-role="title" class="filter-options-title"><?php /* @escapeNotVerified */ echo __($filter->getName()) ?></div>

<div data-role="content" class="filter-options-content"><?php /* @escapeNotVerified */ echo $block->getChildBlock('renderer')->render($filter); ?></div>

</div>

<?php endif; ?>

<?php endforeach; ?>

After doing all steps please clean the cache php bin/magento cache:clean and check in front-end categories page category filer is expand like below image: