Hi Jannu,

Can you try code similar to this.
 

<apex:page controller="AccountControllerfortable" docType="html-5.0" renderAs="{!render}">
    <apex:form >
        <apex:pageBlock >
            <apex:pageBlockSection >
                <apex:input label="Start Date" value="{!startdate}" type="date" />
            </apex:pageBlockSection>
            <apex:pageBlockButtons >
                <apex:commandButton action="{!search}" value="Search" />
                  <apex:commandButton value="download pdf" action="{!Downloadhere}"/>
            </apex:pageBlockButtons>
                    <apex:dataTable value="{!accounts}" var="c" style="border: 1px solid black;">
            <apex:column value="{!c.id}" style="padding: 15px;order-bottom: 1px solid #ddd;border: 1px solid black;" />
             <apex:column value="{!c.name}" style="padding: 15px;order-bottom: 1px solid #ddd;border: 1px solid black;"/>
        </apex:dataTable>
        </apex:pageBlock>
    </apex:form>
</apex:page>

Apex:

public class AccountControllerfortable {
    public Date startDate { get; set; }
    public string render {get; set;}
    public Date endDate { get; set; }
    public List<Account> accounts { get; set; }
    public void Downloadhere(){
        render='pdf';
    }
    
    public void search() {
       
        accounts = [SELECT Id, Name, CreatedDate 
                    FROM Account 
                    WHERE CreatedDate >= :startDate ];
       
}
}

Reference: https://dfc-org-production.my.site.com/forums/ForumsMain?id=9062I000000R791QAC
Let me know if you face any issues.

If this solution helps, Please mark it as best answer.

Thanks,