The blockquote styling provided by the Elementor Text-Editor is very basic. To meet the design specification, the blockquotes can be styled accordingly using CSS.

.single-post blockquote p,
.single-post blockquote p::before,
.single-post blockquote p::after {
	font-family: "SchnyderS-Demi-Italic" !important;
	font-weight: 300 !important;
	font-size: 30px !important;
	font-style: italic !important;
	letter-spacing: 0 !important;
	line-height: 38px !important;
	color: #35393D !important;
	display: inline;
}

.single-post blockquote {
	margin: 82px 0 50px;
	padding: 0;
	border: none;
	max-width: 626px;
}

.single-post blockquote p::before {
	display: block;
    content: "\201C";  /* the blockquote symbol at start  */
    position: absolute;
    left: 0px;
    top: -40px; 
}

.single-post blockquote p::after {
    content: "\201D";  /* the blockquote symbol at end  */
}

Reference

How To Customize Blockquotes Style in WordPress Themes